My problem started with this puzzling AM radio behavior. When the engine is cold I have no AM reception. If I turn off the engine and run the radio from the Accessory position, the AM radio is just fine. Once the engine warms up, AM reception resumes. Also, when the engine is cold and running, turning on another accessory like the heated seats will cause the radio to either play OK or play intermittently.

Based upon a suggestion from a friend, I checked the voltage at the battery under 3 conditions: engine off, engine cold, engine warm. The readings were 13.5, 15.1, 14.8.

My hunch is that the AM signal booster stops working when the voltage is too high. That's OK, and I don't mind not having AM reception until the car warms up, but is 15.1 volts too high? Will it damage the battery (or anything else)? Do I need a new voltage regulator?

All your readings are about a volt too high. Did you verify on another source that the meter is accurate?

No, but that's a good idea. My meter is an old and inexpensive little meter that I mostly use for testing AA and AAA batteries. A fellow in the office offered to lend me his high quality, digital volt meter. But let's assume that the meter is 1 volt too high; that still leaves me with the perplexing question of why the AM radio reception cuts out at the higher voltage.