It varies, per person. If you have dry or often itchy skin, avoid hot as it washes away more natural skin oils. Use warm instead. And maybe use a body lotion right after showering. If you have oily skin, use hotter (not too hot) to clean better. Either way, when you've finished rinsing off the soap, a quick cold rinse to finish is good (helps close skin pores and increases circulation in the skin). This does not mean ice cold, just cooler than room temperature is enough. AM or PM is personal preference, as some people sweat more than others while sleeping. Warm PM showers definitely help for relaxed sleep (and good sleep is extremely important for health), though AM showers are good for a wake-up jolt. So, there ya are. A rambling info non-specific non-answer. Pretty much, it's whatever works for you.
Showering does not have an impact on your overall health. However, hand washing does. It has been shown that hand washing is the most effective means of preventing an infectious disease. Temperature is your preference. Personally I prefer taking it at night because that is one less thing I have to do in the morning.