You may be right, because that's exactly what it's doing. It blew pretty cold for about a half hour or more after the guy left, then went back to blowing lukewarm air again. And the first time we had a guy out to check it, back during a warm spell in January, he said there was too much coolant in it and drained some out, so if he was wrong, maybe it just doesn't have enough coolant.
I don't think anything's heating the air, it's not hot, just not cold. Running it as it is is better than leaving it off because at least it's circulating air, I think. It has a switch for an "emergency electric heat" thing that I've never used because I have gas heaters all over the house for heating.