No, it is not possible to increase the pace at which our body burns off alcohol. This process takes place in the liver, and you cannot affect the rate at which it works.
Taking a sauna, exercising, drinking coffee or any other "miracle cure" might make you feel better, but these things do not affect how quickly the body metabolises alcohol.
Furthermore, even if you no longer have alcohol in your body does not necessarily mean you are okay to drive. Your driving ability can be reduced by up to 20% the day after drinking, even after you have metabolised all the alcohol you have consumed.