This sounds like a bad thermostat, but it could be a bad heating coil, if that's what they use in this unit. You can get parts for it at SearsDirect online:
http://www.searspartsdirect.com/partsdirect/part-model/Hunter-Parts/Air-conditioner-heat-pump-Parts/Model-ALLMODELS/0525/0904000
Since Sear's has sold and serviced this brand, I would call a Sear's Appliance Center and see what they think the problem is. They usually know, or have a good idea, of what's failing, since they're the ones that deal with it.
If you're handy with a voltmeter, you can check the output of the thermostat, and if it's good, then ohm out the coil, or check for a thermocouple, if the unit has one.
I read that they do have a 1 year limited warranty, so you might check into that, if applicable.
Good luck, and hope this helps.