Medication and unhelpful side effects

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I currently take a medication and have to continue to take this medication until who knows when. Problem is, one of the main side effects is that I cannot over exert myself as it diminishes my body's ability to regulate body temperature correctly and reduces my ability to sweat. (which is essential for staying cool while working out).

I guess my question is, if I were to workout in small increments to keep from overexerting myself and causing myself to overheat, how long do you think I could work out for and how many times in a day does any one think, and it still be effective????