Thanks.. What should I tape the door with? Would the glue heat up?

As another poster suggested, patching the hole with silicone caulk is a good
idea.

Just so long as whatever is patching the hole doesn't contain water or other
kinds of molecules that can get excited by microwaves, you shouldn't have
problems with the patch heating up in anyway.

A microwave oven cooks food by exposing it to high amplitude microwave
radiation (also known as radar) emitted by a magnetron. The microwaves cause
molecules inside the food, like water, to move and cause friction within the
food. Because of this internal friction, the food literally cooks itself from
the inside out when exposed to microwave energy and is also why typically the
hottest cooking temperature a microwave oven by itself will ever attain is the
boiling point of water.

This is also a reason why a microwave oven is a cruel and horrible choice for
keeping your pets warm. Remember the urban legend of an old lady who
microwaved her poodle when it got wet? Well, the story may be fictional, but
the end effect is not:

microwave + pet = a dead mess.

- Reinhart