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I'm the proud new owner of a '99 - my first Corvette. Wow!
Problem - The am radio won't work when the ambient temperature is hot. Sounds like the antenna is disconnected. Mostly static. Not engine noise - not rpm related. Just sounds like no antenna.
If you have fm reception then its not the antenna. They use the same one. If you were getting the AM in other cars at the same locations you aren't getting it in the vette you may need a new receiver.