Why should someone with multiple sclerosis not be exposed to high temperatures?

Uhthoff's phenomenon. Ms used to be diagnosed using the "hot tub test": demyelination, or loss of insulation around nerve fibers in the brain or spinal cord can slow or drop the impulse when core body temperature rises. It is reversible, and causes no permanent damage. A patient with ms put in a hot tub may find the legs become numb and heavy, thus needing help getting out!
Temporary worsening. Hot temperatures change cellular membrane capacity to maintain potassium channels, which results in inefficient nerve conduction function, bringing on either new symptoms or worsening of old symptoms. May be termed a pseudo-relapse, and improves with air conditioning, or lowering of body temperature.