What temperature does the luggage compartment of an airplane reach during international flights?

Carry the kit with you in the passenger cabin. You might need to check your blood glucose level during the flight, anyway.

Some holds are heated, some aren't. When they aren't, the temperature can drop very low, and certainly could drop below 36° F. It depends on the aircraft, the location of the cargo, and the flight (pilots have the option of adjusting heat in the cargo hold on some aircraft, when heating is available).

The Baggage compartments on most international flights is pressurized so it would be the same temperature as the cabin but you should double check with the airline you are flying on

my luggage got burned during a flight to florida from Chicago

If you have diabetes you can carry your kit in the cabin with you!

Because there is a needle usually involved I think you have to give it to the cabin crew on boarding, but then they keep it safe for you in case you need it!

Obviously this varies with airlines so check with them first.

The simplest thing to do is to pack it in your carry-on bag. There are no problems at all in doing that. Just send it through the x-ray machine with all of your stuff.

There are both conditioned and non-conditioned holds. You need to talk to the airline to see what can be done.