sounds like overheating but probably something else.. Is it running out of fuel? A mile or two is just about how far restricted flow along with the small amount of fuel in the float bowl will get you.
Ride till it stalls and immediately try a squirt of Starter Fluid.. if it restarts and comes back to life for a moment, fuel flow did stop for some reason. Maybe the gas cap vent is clogged and a gradual vacuum building up in the tank prevents fuel flow... takes ten minutes for it to vent through some tiny crack..
You could try draining (with the gas-cap on tight) a whole lot of fuel into a container .. should be a continuous, thick steady stream until the tank is empty.. if a vacuum were building you'd notice a decrease in flow. If loosening the cap increases flow, same difference.
Or remove the float bowl (or drain the bowl if it has a drain) when it stalls and see if there's any fuel in the bowl.. but the Starter Fluid test is easier..
As far as overheating, the piston kinda seizes from too much expansion. Increased friction absorbs power, eventually stalling the engine. .. won't restart till it cools a bit. Smoke off the head could be just old collected crap burning away.
Remove the head and see if there's lots of carbon build up .. check the exhaust / muffler for carbon blockage which can cause overheating, poor performance..
So can too-advanced timing.. so can lack of lubrication .. dragging brakes or slipping clutch .. who knows.. a whole lot of possibilities.
Get down and do some investigating.. Read through Freds Guide for ideas about what to check..
My guess is it's just running out of gas.. the bike ran good and was in storage .. hard to imagine something mechanical went wrong in storage.