Welcome to the boards!
Overexercising can heat the body up or exhaust the muscle or both. Any of these could be attributable to your concern. You might want to time yourself and then the next time cut your exercise period in half to avoid the problem.
When I start to get tired, I stop and stretch and then I will resume exercise later in the day.
You might try aqua therapy or pool exercises in cooler water. You can get the benefits of a workout without overheating. A trainer experienced with working with MSers is also beneficial. A good trainer should be able to help you develop and set-up a workout routine which will account for your needs. End your exercises with some stretching and a tepid shower. Cold compresses might help with problem areas.
Keep up the exercises, but avoid over-doing it!!