The TC45D doesn't have a clutch. The only driveline "slippage" is when the HST goes into bypass. I think the two most likely culprits are a small leak around the power steering reservoir that is allowing hydraulic fluid to leak down on the hot engine or the under-hood exhaust system has a pinhole leak that is heating something up.
I have a small leak in my power steering hoses (a tiny seep) that allows fluid to collect on the engine. When I work my tractor hard, there is a definite smell of hot hydraulic fluid that doesn't smell anything like motor oil. It is a smell all its own and somewhat like rubber.
You might also check that no foam or rubber is coming in contact with your muffler on the left side of the engine. While there, start the engine and look to see if you hear or see signs of an exhaust leak.
I would also check the fanbelt for slippage. If you shut the tractor down when you smell the smell and sniff around the fanbelt area, you should be able to smell it if it's a slipping belt. You can easily check belt tightness too.