2001 Nissan Quest - smell rubber and heat coming inside car

My 2001 Nissan Quest has been my 2nd car for a couple years - I’ve only put 3000 miles this past year. I let my friend borrow it recently for a few weeks while his car was in the shop. He put about 550 miles on it. I noticed that a rubber smell when I drove it yesterday and popped the hood. It seemed pretty warm there. Then I noticed that very warm air was coming in through the vents and even though I had the air temp turned down. I asked him, and he also noticed the heat coming in the car recently (it just warmed up, so before this week we wanted the heat!). I have yet to find a shop I can be excited about, so like to have an idea what could be going on before I take it to a shop. I cannot afford to get gouged. But I need to have the car in working order since my son’s wife and baby are coming to leave with me when he’s deployed to Afghanistan next month. Can someone give me some ideas what could be going on? (the car has 186K miles)

Drive it around for a while and then carefully feel each wheel for temperature variations. Or if you have something like an infra red thermometer, just use that. You may have a dragging brake - although that often leads to something more like a “fishy” smell, since the car sits a lot this is a common thing to happen. Do be careful - if one is sticking things can get very hot.

Take a good look up and down the exhaust system. Look for anything that doesn’t look right - a rodent’s nest, a lost heat shield, a piece of detached insulation too close to a pipe or the manifold… Especially check the underside of the car above the exhaust pipe all the way down. If heat shields do get compromised, it can get hot enough under there to actually melt the underside of the carpet.

Getting the wrong temp out of the vents is often from problems inside of the duct work, like a blend door problem, but I’m not coming up with burning smell. Someone else might come up with a connection there.

Before you drive it around, check the coolant level.

Leaking valve cover gaskets have been implicated in quite a number of smells. You will probably notice no oil loss, but I would check the valve cover gaskets and spark plug wells for any signs of oil.

Monitor the coolant temp gauge on the dash until this is resolved. If the engine starts to overheat, stop driving. Ask you mechanic to verify that the drive belt for the water pump pulley is in good condition and the correct tension, and that the water pump is turning freely.