Heater has a low pitched rumble

It could be dirt buildup on the squirrel cage blades throwing it a little out of balance. Heaters located near the kitchen area where they can suck in airborne grease particles are particularly prone to build up. The fan motor bushings can fail, but that usually produces a high pitched squeal instead of a rumble. Access to the fans and motor differ depending on the brand and model, but both are replaceable if needed.

I agree coudl be dirt/insect on the blower. can be a bearing going out. they do fail and they are replaceable.

Low pitched rumble sounds like the burner, otherwise I agree with something unbalancing one of the blower wheels. Could just need cleaning, which is actually called for annually.