Running in a car engine is a bit more difficult than a plane engine especially if someone new to engines hasn't yet got an ear for tune. Car engines usually idle somewhere around 6000 so it's not quite like a plane engine in that respect. With a car there's no way to put a load on it unless it's being driven and even then there's not much load so unless you have it tuned quite rich you can't really go full throttle for more than a few seconds. Most car engines can't be fitted with a prop unless you have a lathe although sometimes I've contemplated fitting a couple of props to the axle .

When my son ran in his car engine (and here we go ) he did it using normal 80/20 all castor fuel driving around a grass oval at full throttle but 4 stroking the whole time. That allowed the engine to rev out a bit (I'd guess maybe 20,000) and then slowly leaned it out over 30-40 minutes. We never checked the temperature because that's useless.

As to why the pinch increased in the engine in question (with the head off) I have no idea other than at idle (even at 6000) there's not that much fuel flow which means not much oil flow (especially with car type fuels) so the piston may have overheated.