Retarded timing is more likely to cause overheating, not advanced timing. The timing would have to be so far advanced that it was detonating, and I'm sure you would notice that. Most people only check initial timing, but the only time you are at the initial timing is at idle. Mechanical and vacuum advance add timing at RPM. If one or the other is not working, timing will be retarded and the engine will run hot. Easy to check with a timing light.