sounds like a combination of things..
The heavy exhaust smoke suggests a lot of carbon build up. This could mean the combustion chamber has carbon. A piece of carbon gets red hot and ignites the fuel at the wrong time... backfire.
Carbon build-up in the combustion chamber reduces the compression ratio. This can cause overheating. You might be seizing the piston or there's just a lot of friction.. so the engine must cool a little before it will restart.
Timing should be checked. clean and gap the points (if it has points) and definately use a new, properly gapped plug..
btw, i wouldn't guess about using a leaner mix just yet.. not leaner as far as fuel / air and not 'leaner' about oil mixture until overheating was eliminated as a possibility. Going leaner with fuel or oil means less lubrication and/or a hotter burn.
Whenever you get a new bike the whole thing should be examined.. and pulling off the head is about the first thing i'd do. Just a few bad miles can send a sick engine to the morgue.