Your bathroom having an air vent wasn't a question. If you are using the air vent exhaust from your bathroom, then you are not controlling the lights in a 'no leak' environment. Also, that exhaust has nothing to do with the fan blowing over the plants, nor with the ambient temps. AND, the bathroom exhaust does not 'scrub' smell so when your plants start smelling dank (or should I say "IF"), that bathroom exhaust isn't going to do anything.
Growing in a bathroom cabinet is fine. No problem with that what-so-ever. But if you are going to post threads asking for advise, at least listen to it rather than come back with something like "hey my bathroom exhaust clears the whole room of my nuclear poo, so it should handle the work of venting out my grow".
Good luck on your grow. I hope it is all you want it to be. But for me, it's a waste of time suggesting things like temp gauge and small oscillating fan because you ask for help, and then say you have (sub par) stuff that you claim is working. De-sub'ing.
Ciao