I would hope that like damn-near every other electronic device, it would include at least a thermal cutoff to kill the power before it got hot enough to start a fire.

Seriously, they're in pretty much everything, any sort of tool or appliance with a motor probably has one, of course anything that generates heat like a hair dryer or space heater, I've seen them in lamps, they're everywhere. They're also a pretty common point of failure, so if you're a little handy with a soldering iron, for any random device that suddenly stops working, there's a pretty good chance that the culprit is a brown thermal fuse and can be repaired for just a few cents and a few minutes of mumbling curses to yourself while you try to get the damn thing open.

I think the bigger issue with this is probably people with mobility issues, who I imagine are a pretty big part of the target market for a bed like this, if they have trouble getting out of bed to adjust the heat or whatever, a bed like this is probably pretty attractive. But if they get stuck in bed with the heat stuck on high, that could be a pretty big medical problem.