I have had three fan heaters (two cheapo Chinese ones from Sainsbury, one expensive De Longhi one from John Lewis (got the money back for that one)) in the last couple of years fail because the safety thermostats fail open circuit, presumably from being constantly cycled.
I opened the cheapo Chinese ones up with the intention of replacing the thermostats, but they were not amenable to repair and I was concerned that if I merely shorted the 'stats out, the heaters would burst into flames.