Probably not over heating unless the piston jug is clogged with debris, or the coil is heating up and breaking down not sparking. It could be several things or combination of things. Some things to check, muffler plugged up with carbon not letting exhaust gases out. dirty air filter not letting air in. gummed up carb. not letting gas flow, and outside change weak coil... probably gummed up carb. is my guess.

Just for grins, throw some gas at it and see what happens. IOW, open up the hi-speed needle valve about 1/2 turn. It sounds a little like it's leaning out.
It could also be that the clutch is stopping the engine if there is a problem in the bearing that shows up when the bearing gets hot. Does the trimmer head spin freely when the engine cuts off?
Otherwise, the engine may be running out of gas from several causes or it could be a clogged-up exhaust port and/or muffler as moser suggested.
Additionally, all 2-cycles have a pressure/vacuum seal on the crankshaft where it passes through the crankcase. These seals are critical and must hold pressure/vacuum in order for the engine to develop power. Look for oil/dirt buildup at the seal(s).

Thnks for the advice. I traced the problem to dirt in the fuel that caused the trimmer to run lean. For good measure I changed the plug and filled the tank with Trufuel 50:1. Trimmer is running like its former self now.