Cold water? Hmmmm.....NO! That's the last thing you want to visit upon your scalp!!!!!
Cold water will restrict blood flow to the hair follicles and starve the hair root causing it to die early.
Hair follicle - Wikipedia, the free encyclopedia
IMO the best regimen to wash thinning hair is to wash your hair with baby shampoo (THE gentlest shampoo around) and WARM WATER not hot nor cold just like you would a baby's hair.
Remember, in spite of what all the ads say all you want to do is clean the dirt off your hair and leave some oils behind to protect the hair. Only baby shampoo will do that.