The temperature that cardboard will burn at is any temperature of 400 F or above.
However in most cases it takes temperatures of 800 F or above for cardboard to easily ignite.
Flashpoint and “ignition temperature” and “combustion temperature” are, for all intents and purposes, the same thing, and thus – the flashpoint of cardboard is 800 degrees Fahrenheit.
Cardboard can be used in the microwave for a few minutes of heating food up.
You can also place cardboard in an oven for 5 to 10 minutes to heat food up but just keep an eye on it so that the cardboard does not burn.
I personally though would recommend removing the food such as pizza from the cardboard box and placing it in a more oven safe container or pizza pan.
Cardboard can suddenly ignite when exposed to extreme high heat, however that is very unlikely to happen in a residential microwave.