I have 2 of these temp controllers and I keep both of them submerged in a 44oz cups of water and I have not had any issues. No thermowell is necessary, but if you want to be safe and don't mind spending the time, or money you could do that.
I keep the cup of water close to the better bottles in my fermentation chamber, and next to kegs in my keezer. After 6 months I have not noticed any changes in the functionality of either one of my temp controllers.
In my opinion submerging the probe best way to keep your feedback swing stable. You can also install a fan in there to keep the ambient temp more common vice cold at bottom and hot at top with some changes when cool/hot cycles are started.
Sorry about the heater blowing out.. is there any documentation on it that suggests a period of time that you should wait between on/off cycles... if so you can set this on the controller (compressor delay function). I heat/cool a good sized chamber so I just use a small ceramic space heater I picked up at Wal-Mart for $20, but I don't think that will help you if you are controlling a whole room.