There is some heating that takes place, but the amount is pretty trivial, because there just isn't that much light reaching the back of your eye. A back-of-the-envelope sort of estimate would be to say that the light of the Sun reaching the Earth's surface amounts to about a kilowatt of radiation per square meter. Your pupils have a radius of maybe a millimeter, probably much less in bright sunlight. So, if you're staring directly at the Sun (which, hopefully, you're not really doing), you're getting at most a few milliwatts delivered to the back of your eye. That's not going to tax the temperature regulation systems in your body, given that a living human generates about the same heat as a hundred-watt light bulb.
If you dramatically increase the amount of light delivered to your eye, say by accidentally catching a high-power pulsed laser in the eye, you can overwhelm the body's ability to carry away the heat, and do real damage. The pulsed-laser lab next to the office where I did my undergrad thesis research had a sign on the door explaining in gruesome detail what would happen if you were to catch a full YAG laser pulse in the eye, which involved the boiling retina basically blasting your eyeball out of your skull. Which is why you wear safety glasses in those labs, and knock before entering any optics lab.