It seems to me any unit with a cooler will operate either as "cooling on" or "Cooling not on", but unless it's a really sophisticated unit, I doubt it heats the air to get the temp up.
I mean, if you suddenly jacked up the temp on your fridge, it's not like a heater will kick on to get the temp up, it just won't start cooling until the higher temp is reached.
Now, if that higher temp IS reached but the unit disregards the reading and fails to cool, or it cools down to the temp you set and then continues to cool, there is probably something wrong with the thermostatic switch. I have a portable AC unit that does this. It's either on or off, no actual temp control regardless of what temp I dial in on the control panel...