Indeed not but you still must follow the manufacturers instructions regarding the free air distance around the lamp unit and don't forget what the heat sink at the rear is for - unless you want adidas fingersI even have nice GU10 LED bulbs ready to use. These run very cold. Nothing remotely like scorching 50 watt halogen bulbs.
Unless it's purely for decorative reasons, the lights would be better at the side of, and at the same level as your face. The idea is that they illuminate your face which is reflected in the mirror. Overhead lights will leave your face in shadow.
For good reason the old stage make up mirrors had a row of light bulbs down either side.
Today, modern versions are available, many suitable for use in a bathroom
It is important that they are correctly installed and suitable for the appropriate electrical zone in which they are located.
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