Wow. Thanks everyone for your suggestions. Bishop8 - it's a fire hazard to have towels too close to a baseboard heater. I believe the distance must be 8" between the top of the heater and the bottom of the towels, which should be fine, except for people and kids who fling the towel over the bar so that it slides down almost to the floor. Billl - yes, that's exactly what I want to do, heat the floor surface not so much the air. You said infrared heater. I think of those when I think of the old-fashioned bathroom ceiling heaters you still see occasionally in motels. Are you saying they make infrared baseboard or wall heaters? Do you know any brands you could point me to? Davidro - as I mentioned in my OP, I am not going to pull up floor tile, because I would never be able to re-do the marble floor tile to match the existing marble tub surround and shower walls. Also, this bathroom is an interior ensuite to the master bedroom - i.e. they share the floor structure, and there are no outside walls in the bathroom. But the bedroom floor feels fine, because it is not marble. It is the marble that is the issue, not the floor structure underneath the marble. Birdgardner - I thought of the attic too, which is actually little more than a crawl space above the bathroom. I checked up there again, and it is quite well-insulated. As I mentioned in my OP, you can feel the marble through slippers, and I should have mentioned they are the thick slippers which are normally warm! I am thinking of chucking the whole idea of a heater (and the cost) and getting a thick rug. Maybe I'll post a new thread on this Forum to ask for suggestions for bathroom rugs. Only problems with a rug is that it won't cover the entire standing area, and I am not a fan of rugs in bathrooms because they are dust/hair/powder/sprays traps. I guess there is no ideal solution, but I must weigh the pros and cons of all the solutions provided here. Thanks so much!

if the installer looselayed and nailed the cement board without a thinset base under it, your entire tile installation is incorrect and compromised because he did not give the backerboard a solid base to begin with by electing to looselay it, which is the incorrect method of installing cement backer board. the correct method(s) of installing cement backer board is in a minimum troweled 1/4" bed of thinset mortar UNDER THE BOARDS and nailed or screwed every 6"-8" and within 1-1/2" from all seams, and some manufacturers allow a bed of high strength construction adhesive UNDER THE BOARDS with the same anchors and naiing pattern, so check with the manufactrer for specifics). This gives the tile system a solid foundation to prevent movement and to flatten or level any minor subfloor inconsistencies that may cause movement in the system that can crack or debond tile and/or grout joints. Loose laying and screwing is insufficient and does not provide that solid foundation so it would be prone to movement that can cause cracks, tile pops, debonding, and/or cracking grout joints. The tiles and cement board needs to be gutted down to the bare subfloor, and the cement board anchored properly, or you may have more problems even worse than what you have now. Basically everything needs to be gutted and reinstalled properly or new product purchased and installed properly if they can not be gutted intact and usable. If that isnt feasible for you or your workers, then any repairs may be a waste of time, quite temporary, and plan on revisiting this issue time and time again over the years. Here is some information on CORRECT installation of cement backerboard systems: How to install Cement Backer Board In my opinion, your should demand the contractor with 30+ years experience gut all his tile and backerbaord work, install new the backerboard properly, then the rest of the tile work, PLUS foot the bill for anything that is damaged or uninstallable because of damage during the removal process ... because he did a crappy job and must guarantee his shoddy workmanship. If he refuses, you may have civil recourse becasue his work is improper. as to removing everything unhamed ... good luck ... i dont think its possible because everything is attached and locked in with thinset. If you must try delicate intact removale, jsutt go slow and pry lightly with just enough force to bring it up, but again, its improbable becasue you are talking cured thinset, so i doubt the matting will survive.

Correct, the same, also in matt: https://www.tile-shop.com/products/tuxedo/tuxedo.html So happy with the outcome in our tiny bathroom after the original nightmare, thanks to the help on this site.

It feels wonderful. Another option to think about is a heat lamp in the ceiling just over the area outside your shower. You turn it on when you get in the shower, and are warm and toasty when you first step out and might be cold otherwise. This option can be used only when needed, though it sounds like heated floors also can be on a switch. The two could be used alone or together. You also could add a heated towel rack just outside the shower. Your space and use will dictate your best options and choices for each room. I like to design each bathroom separately so each fits the intended uses and adjoing spaces. Though I like whole house continuity too. Frankly, I'd like my entire house heated from the floor, because I'm a barefoot person. But I can see there no need to heat the broom closet. And it's hard to justify floor heating under flooring that won't transmit the heat well. So yes, think about what your reno guy is saying, but get what you want in the end.