Microwave doesn't work in cold weather

I selected Kenmore because my microwave wasn't listed. It's actually a Panasonic. But hopefully this question isn't specific to the model.

My microwave will not work when the ambient temperature is cold. It will come on momentarily then shut off, as if the power trips out. It's not tripping any external circuit breaker, but it acts like it is tripping some kind of internal protection which then instantly resets itself. If the clock was set before, the time is lost and the display starts blinking, as if you unplugged it then plugged it back in. Sometimes the power stays on for up to 5 seconds, sometimes it just trips out instantly.

I know it is temperature related because if you use a hair dryer to heat up the outside it will eventually start working again. And we never have the same problem in summer.

This may be a common problem because I think the sitcom The Middle joked about having to heat up their microwave in the same way before it would work.

Anyone have any ideas what's going on?