We have one in an antique cupboard (my coffee machine is in there also) with a closed door and we have had no problems. The micro, plugged in with the clock running, is cold to the touch. We do have plenty of space on each side so I don't notice steam from cooking, etc.
We bought the smallest micro we could find to fit. Standard micro, that is. I wouldn't do it with a convection type.

NS, I saved this clip from another thread a while ago because I thought this solution might be something I'd use. If the link doesn't work, do a search for undercounter microwave; it's alku05's post

Here is a link that might be useful: undercounter microwave

On one wall, we had our upper cabinets made 16" deep instead of the standard 12" and put in an electrical outlet. This allowed us to hide a small, 800 watt, Sharp Carousel, microwave. We bought it on sale for less than $100. When it dies, we'll throw it away and buy a new one. It will defrost, heat up leftovers, pop popcorn, re-heat coffe, etc., quite nicely. It does take a bit longer for some tasks, and of course it won't hold a full size turkey :-)

With the doors closed it is completely out of sight. We leave the doors open when in use.

Works for us!

Here is a link that might be useful: Microwave is in cabinet to right of stove

I have a similar setup. It's fine as long as the doors are open when it runs.

If you use it for more than just a couple of minutes, I would leave the doors open for a few extra minutes to allow it to cool down completely.

Super!
Now I just to figure out how deep to make the cabinet.
I'm leaning towards 17" - it might give me few more microwave options. Right now it's between the sharp and the panasonic inverter(?) which are just under 16" deep.

Thanks!

Elizpiz already linked to a thread that shows pictures of my microwave in a cabinet. We paid a pretty penny to get the doors that slide into the cabinet, but they were worth every cent. Otherwise the open cabinet door would stick out or block the adjacent cabinets.

Be sure to look at some individual microwave models and check their specs to make sure you're meeting the needed clearances. Also be careful to make sure the cabinet's inner depth and width are enough. (many 17" deep cabinets will only have 16" of depth in the cabinet)

We did something similar. We took the doors off the cabinet and I made a built in look. It is on the backside of the island so no one can see it unless they walk around to that side.
The best fit for the space was a Panasonic Inverter. So far it has worked very well. It is 1300 watts so it cooks much faster than our old OTR micro.

Just saw this post and this is exactly what we want to do, just like alku05's MW, only in a higher cabinet. Does anyone know how much space is needed around the MW if it is set inside a cabinet with doors? Thanks

It depends on your particular microwave and cabinet brands.

You'll want to look at the spects for your microwave and see what the side, back and top clearances it requires are. Once you have that info, you need to make sure the cabinet walls and slid-in doors are at least this difference away from the microwave.

Where the cabinet brand comes into play is how much room the slid in doors take up, and whether you want/can get doors that slide-in on the sides or on the top. We wanted a door that would slide in the top, but our cabinet company only offered doors that slid-in on the sides.

Our cabinet is a 27" base cabinet, excluding the width of the cabinet walls and slide in assembly, there is 22" of usable space (according to the cabinet company). The ventilation room is slightly bigger b/c the doors really only occupy part of the asslembly space. This means that our 20.5" microvave fits in there with 2" of clearance space between its sides and the doors when they are slid in, which complies with the microwave's specs.

we did ours in an upper corner cabinet and have had no problems with it. we keep the doors open while cooking and for a few minutes afterwards. plenty of space around and behind for air to circulate:

Awesome,Edlakin and Alku05! Alku, I appreciate all your info. We will take both of your pictures to our cabinet people tomorrow. Edlakin, what size is your cab and MW? Thanks so much.

Edlakin, Can you tell me the size of the corner cabinet that you put your microwave in and the dimensions of your microwave? Could you post or email a picture of the whole wall that the microwave is on? Thanks so much.