It’s the reversing valve most likely ($200 avg.) or it’s not getting the signal to turn the compressor off / heat strips on when temps hit 35F. Also, the reverse cycle may not be long enough, which would be a bad controller board ( $239 avg.)
A good heat pump turns the blower off basically and runs the unit in AC mode a bit for defrosting, but it’s the reversing valve that usually sticks...bad solenoid usually and most are built in. They have to be removed by a a pro and then silver soldering the new one back in-line by a pro that can recover and filter the freon, pull the vacuum on the system and then recharge the lines with the correct amount (lbs) of refrigerant.