See this previous thread. Answers depend on your climate.

"Skim coat" of what?

Insulate the perimeter walls per code or more to a certain distance below grade depending on how cold your climate is. There is little reason to insulate the ground but if you do it wouldn't need to be much since the temperature of the earth shouldn't drop below the temperature of well water.

What is a new 70's house?

New to the poster, I take it.

Skim coat is concrete. House is new to us. Converted a crawlspace in a house we built in '75 from ventilated crawlspace to heated crawlspace a few years ago and the heated is vastly superior. In that case I just used the white, 3" styrofoam off cuts from a LOGIX insulted concrete form project. Before I added the styrofoam I couldn't get the crawl space up to 72 f with a 500 watt electric heater, With the styrofoam it is not a problem. My goal was to have warm floors and that was achieved. With the house we just bought I wanted to achieve the same result. Just wondered if anyone had a more elegant solution to the insulating problem. Yes its only 55 f on the ground but that is a powerful radiator of cold. I don't think 55 f floors are very comfortable underfoot.

The house is in the pacific northwest

Ok, this is a remodeling project rather than a home building project.

A sealed crawl space is required to be ventilated from the house to avoid moisture build up and a heater in the crawl space would not provide that. Also, ventilation air returning to the house raises the issue of thermal protection of the exposed plastic foam in the crawl space. You need to read the code requirement options carefully. Rigid mineral fiber insulation board might be a better choice..

The floor above is radiating heat to the cooler slab. Forced warm ventilation air would transfer heat directly to the slab. If I were going to heat an insulated crawl space I would rather use forced water fin tube radiation and foil faced rigid mineral wool insulation on the slab below in addition to the ventilation air. There are also sealed element electric finned heaters.

I don't know the location of your house so I can only refer to the most commonly adopted residential code: the 2012 IRC.

To omit exterior ventilation openings in a crawl space the code requires

1) continuous mechanical exhaust of 1 s.f./ min. for each 50 s.f. of crawl space with a makeup air pathway to the common area (duct or grille) and perimeter wall insulation as required by the energy code.

2) conditioned air supply of 1 cu ft for each 50 s.f. of crawl space with a return air path to the common area and insulated perimeter walls.

The only exception is if the crawl space is an existing plenum.

If you choose to insulate the crawl space floor with plastic foam board, the 2012 IRC would require that it be covered with 1 1/2" mineral fiber insulation (batts or rigid boards); 1/4" wood structural panels or 3/8" gypsum board but you shouldn't put wood or paper in a crawl space.

Even if there are less strict requirements in your jurisdiction I recommend you use these requirements since it is a life safety matter.

And I would not put an electric resistance heater with an exposed element in an enclosed unsupervised space. You might also install a smoke detector in the ventilation air path.

And be sure to use a radiant barrier as the top layer on the floor. The best insulation would be foil-faced foam insulation boards that have passed the thermal protection test. I doubt you would need more than an inch but you could put a cheaper insulation under it.

Also, without clear evidence don't assume the slab has a vapor retarder under it. You might install one before the insulation or use the radiant barrier or tape the foam boards.

The most serious issues are fire safety, moisture removal and insulation in order of decreasing importance.

not an expert on cold climates....but wouldn't you just insulate

the undersides of the floors with closed cell foam insulation?

"And be sure to use a radiant barrier as the top layer on the floor. The
best insulation would be foil-faced foam insulation boards that have
passed the thermal protection test."

we do radiant barriers in my hot humid climate...but in attics.

in any case a minimum of a 3/4" air space has to be maintained

for rb to work.

to achieve this spacers would need to be between the underside

of the floor & the reflective side of the foil. easy to recommend...

harder to actually install correctly.

just my hot humid climate thoughts!

The OP is asking about heating a crawl space in a cold climate.

The point of the conditioned crawl space defined in the IRC is to maintain the free flow of cool or warm dry air throughout the space and especially around wood joists where mold is most likely to grow. Therefore, insulation in the floor joist bays is contrary to the conditioned crawl space concept not only because it restricts air flow but in a cold climate it could allow surfaces to cool enough for condensation to occur although adding enough heat and insulation at perimeter surfaces might prevent that from occurring. Also high density closed cell spray foam would be very expensive for this condition but might seal the joist bays enough to prevent mold growth as long as it doesn't shrink away from the joists. Another advantage of not insulating the joist bays is the ability to inspect them for mold growth. But the most obvious reason to not insulate the floor with spray foam is that it would not increase the temperature above the floor to the level desired by the OP and the foam would need to be protected against ignition with mineral wool or an intumescent coating which further increases the cost. Since the code requires insulation at the perimeter foundation wall the only p;ace insulation should be added is on the slab where the heat loss is.

The radiant barrier should be on the slab on grade or the top of the insulation on top of the slab rather than between the floor joists so it won't prevent air flow in the joist bays. But since the temperature difference between the floor above and the slab is not terribly great, it would not make much difference if the radiant barrier was omitted. I just thought foil-faced foam board might not only save energy but also meet the code requirement for protection against ignition since the alternatives (gypsum board, hardboard. particle board, OSB & plywood) would not be appropriate in a crawl space. However, as noted earlier, 1 1/2" or thicker rigid mineral fiber board would work on top of foam board or by itself.

Still not sure where the house is. The Pacific Northwest covers three distinct climate zones.

If it is in the Marine climate, as I referenced in my first response, a vented crawl works well. In that case, just separate the two spaces.

If it is to be conditioned, the link below to a paper from the Oak Ridge National Laboratory notes the importance of power venting radon from the crawl rather than just connecting it to the house HVAC system.

http://web.ornl.gov/sci/buildings/2016/2010%20B11%20papers/174_Hales.pdf

Thank you for the advice. I have been concerned about the fire hazard with the ICS foam and will check my local bylaws. I will checkout the rigid mineral fiber board. I was also interested in the polysi foam board. thanks again.

Polyiso will provide the most R value for the thickness but that may not be important unless the space is short. However, the foil facing may satisfy the ignition barrier requirement and avoid the need to add mineral fiber board (I would provide a barrier even if not required by your code). I would call the manufacturer and ask if their product has been tested.