Hey Ben,
The first thing I would check would be the function of the Cooling Fan! As a rule, these bikes will run pretty close to normal if you were making a highway run because of the air flow over the radiator. Around town, (stop and go traffic) is where your cooling system depends on the flow of the water pump and radiator fan. Are we to assume that the coolant is 15+ years old?
Another thing to consider is your bike poorly tuned? (Carb. Sync., "Crusty Plugs", gummed up Carbs., etc.) You didn't mention mileage. Even things like low tire pressure will put extra load on the engine while riding, and tax the cooling system. All things to take a look at.
Good luck with this project, Ben!
Earl