[TibetanT]

I am certainly not an expert, but you might want to check your Heater Control boxes at the rear.

You may have allowed rodents to get inside if the hoses connecting the heat exchangers to the tunnels are 1) destroyed, 2) old and completely gone, or 3) the heater control box is left open.

Mice love to make nesting sites on top of the engine under the shroud. Most engine tear downs that I have done for others entailed finding nests on the top of the heads and cylinders.

I would guess that the other spot where mice can chew and get in would be in the trunk area since those are paper hoses for the ventilation.

Dryer sheets should deter those pests from coming near those hoses during the Winter months when we, Northern States, park our P-cars.

As far as the burning smell…hmm? Not too sure why that is happening, but you may be correct that something is inside and getting burned/heated/torched.

Hope this helps.