How can I measure the temperature wirelessly inside a piece of meat?
Unless you're into eating charcoal, the temperature inside the meat should never exceed 170°F (75°C) which is within the Industrial/Automotive range of -40°C to +85°C. So you can get electronics that will survive; the problem is how do you power that. I know you said you prefer a batteryless solution, but there are NiCd batteries that are rated to 55°C. See high temperature nicd cells

I've heard of chemistries that work at higher temperatures but don't know exactly what they are. 

A batteryless solution to this would be interesting. I'm guessing from your description that you can't get closer than about 6-10" (150mm to 250mm) from the food, which makes inductive powering difficult without wasting lots of energy. Wonder if there's a way to get energy out of eddy currents.