White smoke from driver's side vent.

I definitely had smoke coming through my HVAC system when coming to stop. After the car sat for a few days, enough oil would drip onto the exhaust manifold and during the first few miles the smell was drawn into the cabin during each stop through the fresh air intake. After a few miles the oil burned off and the smell went away.

There wasn't enough oil leaking to even reach the garage floor and finding the leak took some detective work...luckily it wasn't the cam tower seals as I originally thought. Cam seals were perfect too. It was the large donut type O-rings and small bushing seal behind each cam assembly.

Very cheap and very simple to replace on the 16V motor.

^^^^^^
Regardless it wouldn't smell like PAPER burning... Oil, paper and plastic (from wires) all have VERY different odors! Not sure WHAT we have in the car that might actually smell like paper burning though!

If you are getting oil smoke/odor into the HVAC system, check the hood seal at the rear of the engine compartment. There should be a rubber seal clipped to the top of the firewall at the back, holding down the (fragile) black plastic cover at the base of the windshield.

Another possibility for burning odors from the HVAC...
If you get a leaf into the HVAC inlet (base of the windshield, passenger side, under the black cover), it will often get onto the resistor pack located in the HVAC plenum. This resistor pack enables the varying fan speeds, and has several large nichrome wire resistors that get very hot when the fan is on low speeds. The burning leaf will cause smoke and odor, but will burn away quickly, and virtually never causes any problems.

just a thought.
You have the stereo cross-over in the door, maybe you have something going wrong in there and you may want to pull the panel unless you are sure it is from the vent.

also if the tube under the dash is disconnected you may have something going wrong under there. You need to trace it backwards.