Q: Car vibrates in drive or reverse at high temperature

If the engine is vibrating (as opposed to the drive train axles, wheels, etc.) that points to an "engine management" problem. This includes a cylinder compression imbalance (variance in compression pressure) or an ignition, fuel system or air induction problem. Although, at 80,000 miles, you don’t have a lot of miles on the engine, typically the engine compression is checked initially just to be sure the vibration is not due to a mechanical fault like sticking valve(s) or leaking rings.

If the compression is OK and there is no excessive variance from cylinder to cylinder, a diagnostic scope is used to determine what is going on within the individual cylinders. This could be from a bad plug, wire, coil, injector or you could have a "global" issue like a bad mass airflow sensor, coolant temperature sensor, fuel pump, and so forth. If you would like to have this checked, a qualified professional from YourMechanic can come to your car’s location to diagnose the vibration issue and pinpoint the possible repairs.