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I Have a Craftsman Mower with Briggs and Stratton motor 310707 - as soon as it starts it gets extremely hot the muffler get extremely hot and smokes

please advise ,

When you say as soon as it starts do you mean in 10 seconds or 10 minutes. I am thinking right off the top of my head that the valve cover gasket is leaking and dripping on the muffler and you are smelling and seeing the oil burning off the muffler.

Sounds lean. Clean and or replace parts of the fuel tank to carb. Adjust valves. Get some UV dye and find/fix your oil leak/s.