Is it normal to get strong headaches when being in cold/hot weather? I get this sensation/feeling of my brain over heating or being cold.

Not your brain. Your brain is well-insulated from outside temperatures. More importantly, though, extremes of temperature could be triggering your headaches. Keep a journal of when your headaches occur, trying to identify your headache triggers. Also remember to stay well-hydrated, as dehydration plays some role in up to 60% of headaches. See your neurologist, and good luck!