Yeah putting it on top of a heater will probably cook it.
I see you've had a variety of responses - but the sum of it is cheap DPSS lasers essentially do this. My own ones do the same thing - you press button, it goes bright, then dims, and then gradually brightens again.
Were you in a cold room? This will make a great deal of difference. When I did stress tests on cheap DPSS lasers exactly like this, they took a full minute to "warm up" to a point where I could see the beam, and this was in a chilly room at about 10-14degrees C.
If you just want something to point around and have a bit of fun with you don't necessarily need a proper laser, but if you do buy one I wager a fair bet it'll get you interested in the hobby proper.
Room is around 20C, It usually works now after it cooled of. I see I just bought a shit laser and will look into buying a proper one.