When running hard (road race or triathlon) the right side of my tongue often goes numb. It goes away shortly after I stop. Any ideas why?

Only a wild guess that you have nerves in your neck/jaw/face that get pinched when you run, perhaps from the way your neck is jolted or some way you clench your jaw muscles. I would ask this on a runner's blog site.
Since it goes away and doesn't hurt, I doubt that a doctor is going to want to run a lot of EMGs, which are painful and may not even find the source, since you can't be tested when it's happening.
Test yourself by running with a neck brace and keeping your mouth open, etc. Run in place in front of a mirror or someone with a movie camera to see what you are doing with your mouth when you run. Think of the way an arm goes numb if you sleep on it.