This is exactly what was going on with the system here when I moved in. I'm a dummy with the HVAC stuff, but I recall that the tech said there was likely a leak in the system somewhere. They could have spent time diagnosing and tracing, which he said could be cheap or expensive depending on where the leak was and how long it took to find it, but for a variety of reasons I went with a new HVAC system.
Anyway, same as yours - checking with an IR thermometer, It was blowing like 70deg and wouldn't go higher. Which of course wouldn't get the house anywhere near 70deg. Another possibility might be it's stuck in defrost mode? That would blow cool air as well. Definitely check the temp at various registers with a thermometer though.