I'm sure there are many parameters to tune, although I don't know the details. But a "heat pump" is just a machine that pumps fluid in a certain way to make one

I'm sure there are many parameters to tune, although I don't know the details. But a "heat pump" is just a machine that pumps fluid in a certain way to make one end hot and another end cold. With a traditional AC, the hot end is placed outside and the cold end inside. What the HVAC folks call a "heat pump" is a particular variety that can reconfigure itself to put the hot end inside. If you were so inclined, you could heat a space by taking an AC and turning it backwards so the hot end was inside. (This would be pretty dumb unless you needed to heat stuff up in the summer, since the temperature range it's built for would be all wrong otherwise, but it works.) I'm sure there are heat pumps that don't cool well when the temperature is too high, but I don't think it's a general property of all of them.