Sorry to hear you are experiencing such an extreme reaction to heat. We MSers do generally find heat difficult but I have never experienced anything as bad as what you describe.
You can get both a cooling vest and a cooling neck tie which you might find helpful. If I am desperate I pour a little water from my water bottle down my T shirt . Seems to work for me. I am sure some others on the board will come up with some good suggestions.
Have had relapsing/remitting MS since 10 yrs old. Secondary/progressive since 1995. Baclofen pump since 2008.
"The past is history, the future is a mystery, the present is a gift."