Wife and I have slept with a noise generator under the bed for the past ~10 years. It’s on a timer, set to run it from about 11PM to 8AM, so at this point it’s probably accumulated about 33,000 hours of operation. A couple of nights ago, in the middle of the night, I noticed the sound level was fluctuating. The next day I took it apart, and as expected, it’s just a fan powered by a cheap induction motor fitted with Oilite bushings. I added oil to the felt reservoirs and put it all back together, and it seems to be working fine now.
It occurred to me that if the rotor really did completely seize up in the middle of the night, this thing could potentially overheat and start a fire. A fire under a bed in which I am fast asleep seems like it would probably be sort of bad. I didn’t notice any kind of thermal switch/fuse in there, but I don’t know how subtle such a thing would be. Is it common for induction motors to be fitted with an overtemp cutoff of some kind? Maybe something really integral, something small that I might have easily overlooked? Should I consider switching to a solid-state noise generator?
Your link says the device is UL listed, so it shouldn’t be a fire hazard if it seizes up. I imagine that means it does have some kind of fusible link somewhere and yeah they can be small. I suggest oiling it more often, say every three months or so, just to be on the safe side. It’s also a great idea to have a smoke detector in your bedroom as well.
Alternately, you could get a gaggle of kittens … not as much of a fire hazard and still produces noise between 11pm and 8am …
I have used one of those for years. Not under the bed, but beside the bed on a nightstand. Perhaps you could consider moving it. It might give you a slight advantage.
The advantage being if it seizes up and starts smoking/sparking you’d wake up faster? 
I’ve used such a device for a long time and never had a problem.
Here comes the light - what a fine morning to mourn.
I mourn the night without a sleep-sound.
Yes. In the unlikely event it should malfunction and cause a fire, I would rather have it beside the bed than underneath it. I have never had a problem with mine either but the op apparently is.
My entire family uses there (us, and the kids). I never worried about the fire hazard bit until this thread. Thank you for that. 
I would guess the risk is low. If you are seriously concerned, buy a new one or, as suggested, move the device to a bedside table. Flames will tend to burn up, so NOT having it underneath your mattress would be safer.
Does that work better than the easily downloadable and free apps that are available?
How dirty was it when you took it apart? I’d be surprised if it didnt accumulate a bit of dust after ten years of use. Periodic cleaning would reduce the risk. Do it once a year when you clean the dryer vent and change the smoke detector batteries. You know, that day that you are supposed to do that sort of stuff but never do.
You could also add a thermal fuse. You can get them very cheaply online in a variety of temperature ratings. Only problem is that they have to be inside the device. You’ve had it open so you have a good idea if you could add one or not.