A complete model number may help others help you.

Which thermostat, most units have two?
The main temperature control thermostat and the defrost thermostat.

Do not understand why you are letting it defrost???
If it is not working then you should not have any frost.

After a manual defrost the unit should work OK until the evaporator coils heavily ice/frost up again, usually a couple days.

Check to make sure the fans and compressor are running.
If not the unit may be stuck in a defrost cycle.
The tech may have forced a defrost and the timer is not advancing out of defrost in which case it is toast.

Also do not understand why the Sears tech said to leave it for a couple hours before trying the unit.
If the problem was the temperature control thermostat, then it should do it's job right away.
If it was the defrost thermostat then they were letting it go through a manual defrost. If this was the case it indicates that there was ice in the freezer section and they could have frozen the thermostat, forced a defrost and checked that the defrost heater came on. If not then either the heater or the defrost timer is toast.
Note that there is a possibility that you had 2 problems. The defrost thermostat was shot but also the timer or the heater is shot.

Are the compressor and the fans running?

If not you may be stuck in a defrost cycle.

If the compressor is running (warm and vibrating) and there is no cooling at the freezer's evaporator coils, then either the compressor is toast or you are out of freon.
In either case it is an expensive repair and often makes more sense to put the dollars into a new unit.

Note - The freezer started to get cold after we plugged it back in a few hours after the tech left as he instructed us to do. It then started warmng again... ice never did freeze??