Taking the mic! 1/2 hour tops, compression test is just a basic check to see if one cylinder is down, and so could indicate a badly blown HG, broken piston ring, badly seating valve, or worst case scenario hole in piston.
However I recommended a leak-down test as this will differentiate between a valve seat problem and ring seal/head gasket, before just dismantling things to find the cause.
But based on what you have said about the engine overheating I would be looking to replace the head gasket/s.