Trying to make a resistance wire heater to fool an air conditioner's thermostat.
Yes, it should be possible.  No, it doesn't sound like a good idea.

Regular residential air conditioners are designed with some assumptions, including a lower limit on the temperature to cool too.  The unit might work very inefficiently, or not at all, at a temperature much below what it is intended for.  Icing will also quite likely be a problem, unless maybe you are in a very dry environment.

It sounds like you really want a refridgeration unit, not a air conditioner.