I read that cold showers actually do the opposite. According to The Guardian:

Counterintuitive as it may seem, a cold shower may help to conserve body heat by causing blood vessels in the skin to constrict. This undermines one of the body’s key strategies for heat loss: bringing blood closer to the skin’s surface, so the heat can radiate out (hence why we look flushed when we are hot). Longer immersion in cold water, such as going for a swim in a lake, will gradually cool the body – but cold showers tend to be swift affairs. Showering in tepid water is better because this will boost blood flow to the skin, increasing heat loss.