As long as the shutter was closed the sensor itself would be protected by the shutter curtain from the light of the sun. I have heard of shutter curtains being damaged by sunlight, but that is usually in the context of a powerful telephoto lens being mounted to the camera and pointed towards the sun on an older camera with cloth curtains. On the 5DIII, the semi-translucent part of the mirror allows light to pass to the Auto Focus sensor array. There is a small chance that too much light could damage the focus array, but I doubt unfocused sunlight when there is no lens mounted could do so.

What I would be more concerned about is damaging the mirror. It is the most fragile part of your camera and should never be touched on the surface. Unlike most mirrors in other applications that have the reflective coating on the back of the glass, the mirrors in cameras have the coating on the front surface and it is easily damaged. At most, use an air blower to gently knock dust off of the mirror.

Addendum:

Lensrentals.com has posted a blog entry in which what happened to some of their rental equipment that were used without proper solar filtering during the August 21, 2017 total eclipse in the United States is shown in photos of the damaged equipment.

Damage to a shutter curtain, presumably this happened during use of mirror lockup:

Damage to a sensor:

Damage to the aperture diaphragm of a 600mm f/4 when the user used a rear positioned drop-in solar filter: