How much smoke? A wiff or enough to depress the local mosquito population?
Have you allowed the mower to keep running after it starts smoking? Does the smoke clear with time?
Exhaust parts simply WILL be hot. It's not uncommon for exhaust internals to reach dull red heat. A small engine with the muffler removed will sport a 4-8" blowtorch like flame at the exhaust.
Now, to the smoke... First thing to do is check the oil level. Overfilled oil is the most common cause of smoking. The oil could be overfull from previous servicing (ie. accidental overfill by service guy (maybe that's you)), or it can become overfilled as a result of a gasoline leak in the carburetor. This is likely the case if you find the crankcase overfilled, but you know that it was not overfilled during servicing. In this case, the oil may smell gassy.
Sometimes even parking a mower on a slope such that the cylinder is "low" can result in smoking at startup. This smoke will generally clear in a minute or so. What happens is oil seeps past the piston rings while the motor's shut down, and pools in the combustion chamber. Upon starting, the oil is expelled into the muffler. Then the muffler gets hot (in a few seconds) and the oil burns off. This would be no cause for concern if the oil level is OK.
If it's neither of those, it could be simple wear and age. How old is the machine and how well has it been maintained? These engines will begin to smoke as they get significantly old, especially at startup. If the smoke clears in a minute or so after startup, and oil consumption is less than about 1oz/hour, then it is not serious and can continue to be operated. The only hazard is glares from the neighbours.