I also run the AtmaSphere M60 monoblocks. I have always run them with a full complement of tubes.
As far as heat goes, I am not sure if any amps exceed their capabilities to heat a room. Yes, they run hot, hot, hot. As Rush pointed out, they are pure Class A. That means heat and a lot of power draw.
The only other negative I can think of is that they do not grab hold of a woofer's voice coil and shake it to the ground. Although the bass they do put out is nicely extended, and exceptionally tight.
Also, some may find the sound a bit too clean and pure(I have a friend who feels that way).
On to the positives.
You ask if they are stable. Well, how do you feel about the anecdotal stories about Ralph Karsten shorting the amps with a quarter when asked this question at a show, only to have the amp not harmed in any way? I can tell you that while I have never witnessed Ralph do this, I believe it to be 100% accurate. I am embarrassed to say that more than once, while moving the loudspeakers around to get that last bit of performance, I have discovered no sound coming from a speaker. Only to realize the reason was that I have now shorted the stiff loudspeaker cables on the speaker binding posts. As soon as I correct the situation, all is fine, and the music resumes. Are there many other amplifiers, OTL, tube, or solid state that are that bulletproof to the point of not even blowing a fuse???
Next to an autobias amplifier, this is as easy as things get. I can literally bias both of my amps in about 2 minutes.
Ralph's mantra is the "20 Year Rule". What he builds should be around for at least twenty years. Every element in his thought process follows that rule. Hence, his choice of the 6AS7G output tube. This tube has earned tremendous respect in the field by the Eastern Bloc countries who have used it in their military applications. I know that from a Russian person I work with. They don't have much in the way of a more rugged tube. As has been mentioned, in the AtmaSphere amps, they can go for a long, long time.
The tubes are also very low cost. I have routinely seen dealers sell them for between $6 and $15 new. Although, the more official price of the Sovteks are about $16-$18 and $22 - $26 for the Svetlanas. Please note also that there is no difference whatsoever in the two brands, they are manufactured in the same plant. Some feel that the Svetlanas are a bit better due to going through more QA/QC, but no one knows if this is really true. Supposedly, people who have A/B them in every way can see or hear no difference at all.
In summary, I am not sure one can find a more rugged tube amplifier than AtmaSphere.