Will use of drugs make you sweat?

Caffeine does make you sweat. Caffeine is a stimulant of the sympathetic nervous system, which, amongst other effects, increases sweating. (Part of the fight-or-flight system, the sympathetic nervous system is why you get sweaty palms when you are anxious). As an aside, a strong cup of coffee used to be given as a treatment for Asthma as it widens the air passages in the lungs, acting as a stimulant of the sympathetic receptors there. The equivalent modern treatment is the drug theophylline, a caffeine related substance that is found in tea. The previous answer mentioned caffeine's effect on anti-diuretic hormone (ADH). Caffine inhibits the action of ADH thereby causing an increase in water loss from the body and increasing the frequency of urination.