Hot water bath

Is it good to have a hot water bath after a workout for building muscles?
It has barely any effect on your muscle growth.

But cold water showers have been proven to burn calories (not a significant amount though).

Hot water baths are relaxing or comforting whereas cold water baths are refreshing.

If you are on a heavy weight training routine, a hot water bath would be quite beneficial as it reduces muscle soreness, improves blood circulation and induces a sense of comfort or ease that helps in getting a good sleep.

Another major reason is that, after a workout your body temperature is usually quite high and having a cold water shower shocks or stuns your muscles. Having a hot water shower prevents this stun effect. Sudden drop of body temperature may cause fever or any other form of weakness.

Overall, after a weight training routine, having a hot water shower would be better than a cold water shower.

Cold water bath

Cold water prevents the swelling and typical pain which sometimes happens after any strenuous workouts. Cold water shower works in the same way as the ice pack will work for a post workout injury. This also helps in increasing the blood circulation in the body.

Cold shower after a sweaty and hot gym is a shock to the system. The immediate drop in the body temperature directs the blood flow towards the vital organs which leaves the muscles alone to repair and manage with the lactic acid accumulation which has happened. When this happens, vasoconstriction takes place (Vasoconstriction is the constriction of blood vessels which increases the blood pressure) which reduces the temperature of the damaged tissue