Purchase a quality anti-fog solution such as Rain-X. Moisten a paper towel or cotton cloth with the anti-fog solution that you chose and wipe clean the mirror in your bathroom with it. Irrespective of how hot your shower is, fog will not be able to accumulate on the bathroom mirror and it will stay clear for at least a few months after you have applied this treatment.
Another way of defogging bathroom mirrors after a shower is to make use of a hair dryer. Set the hair dryer at the hottest possible setting. Hold it approximately 6 inches from the mirror. Maintain the distance between the mirror and the hair dryer and move the dryer along the boundary of the mirror first and then around the middle part. Fog will quickly evaporate and you should be able to defog the mirror within a few minutes at the most. A major disadvantage of using this method is that you have to repeat it each time after you are done taking a hot water shower.
Consider using after shave solution or shampoo to clean the mirror. This is a relatively old method but a very effective one. Apply an appropriate quantity of after shave solution or shampoo to a towel and wipe clean the fogged mirror with that towel. Although you would be able to defog the mirror easily, it will fog once again as soon as water vapours get onto the mirror.