Interesting, similar thread yesterday... Heat mats, improperly used, are VERY dangerous. If they are sandwiched between solid surfaces, they will overheat and do damage - or burn your house down! It doesn't necessarily relate to thermostat failure either. Most manufacturers suggest leaving an airspace between the bottom of the enclosure and the surface it sits on to allow air circulation so they won't overheat. Put the mat on a table, and the enclosure straight on top, and bingo - instant hot spot.
Heat cords are DEFINITELY the way to go. Wouldn't touch a heat mat these days...
Jamie