smoking coming from 1999 Nissan Quest

I just bought a 1999 Nissan Quest with plenty of miles (over 217k). We didn’t notice anything on the long drive home, but since have noticed that after a few minutes driving, it has smoke coming out of the engine compartment. It’s not noticeable until the vehicle is parked, so far (i.e. it’s not belching out to the degree we can see smoke while driving, but perhaps that’s because the source is low). When the vehicle has been running a bit, the engine compartment does seem unusually hot.

(I don’t suspect any problem with the cooling system itself though. The thermostat was changed this spring, the coolant level is fine, and there are no other signs of overheating, including the temperature gauge.)

Also, and I’m not sure this is related or not, but there is a sound that occurs when accelerating, too high pitched to call a click.

Given that the smoke seemed to be coming from near the back of the engine compartment, I initially thought to check the transmission fluid, although I didn’t really think that would cause smoking. It was indeed low, but topping it up did not solve the problem.

I also wondered whether it might be related to the timing belt (I hope not!), but I’m not reading these sorts of symptoms relating to timing belt wear, and while I do get a burnt smell, I doesn’t really recognize it as rubber, so….

Another possibility I thought of, since the smoke comes out underneath in the neighbourhood of the wheels, is that the brakes are catching just enough not to impede acceleration but enough to smoke. Not sure if that’s the right smell either, but it may be. Kind of hope it’s that, since the vehicle needs brake maintenance anyway (braking feels soft, and brakes are usually something I want to deal with when buying a used vehicle).

Any thoughts?