Yes, gets hot. These are being used more and more. For awhile now in PSU for computers. Finding more applications elsewhere.
Soft starting your compressor will put less load on the motor, does not spin up as fast, far less current inrush = less component stresses. May help it last longer.
If I did this, would place it on the hi pressure cut out switch, like screw down one lug and solder other wire to other lug. Or I would make a small pcb board attach board in the electric box above the hi pressure switch.
Also was mentioned, you can make a circuit that bypasses the NCT resistor once motor spins up, then it is only used for starting the compressor.
https://www.instructables.com/id/Con...ed-by-Large-T/
Cooldown time is about 2 minutes. So if you shut it off, and immediately restart, then very little amp draw improvement over not having this.