Absolutely. Heat as an exacerbating factor of MS is well known throughout the neurology literature and by MS patients. It's called Uhtoff's phenomenon and MS patients can tell you that their symptoms of blurry vision or weakness/tingling of a limb are brought out temporarily by a hot shower or summer day. It's thought to be due to a sensitivity of damaged nerves to increased temperatures.
YES, YES, YES! For a lot of people with MS heat can cause problems. It is usually temporary and as soon as you get out of the heat and get cooled off the symptoms will eventually subside to what you had before you got into the heat. Heat can exacerbate your symptoms, but usually does not cause new ones. I would stay out of the hot tub!