This is just off the top of my head...
Hotter core? Radioactivity - this is the only way I can think of to maintain a hot enough core temperature to provide energy for surface life over geological time periods. The organisms would then have to be resistant to the radiation.
As for the lack of photosynthesis, the earliest unicellular life on Earth did not use photosynthesis (there was no oxygen way back then) - they were chemotrophs (https://en.wikipedia.org/wiki/Chemotroph
). More advanced life could possibly develop using these as a food source (e.g. https://en.wikipedia.org/wiki/Myco-heterotrophy
) but I don't know if you would get any "animal" life able to survive this way. Maybe a biologist could comment.
EDIT: I've just seen the spam link in your signature for a site that promotes academic cheating. Reported as spam.