RE: puher/puller
The exhaust gasses maybe a few degrees cooler than the engine head, actually they might be even more than that due to the fact that head heat is causing by the combustion of the fuel, and friction between the cylinder and the piston. However, lots of oil, unburnt fuel and the sort is expelled by the exhaust, to direct this onto the engine head would create a huge mess. If you are really concerned about cooling install a water pickup and wrap a coil of copper tubing around the head.