Are there any organisms that perform photosynthesis-like processes with thermal energy alone?
Thermophiles are organisms that are capable of surviving high temperatures. It doesn't mean they use or harvest the thermal energy in any way. Normally proteins start to unfold and degrade at temperatures above about 41 °C and all other organisms have a hard time coping with the effects.
Usually biology uses chemical energy. Photosynthesis is the one exception of a biological system converting the energy of photons directly into chemical energy stored in complex biomolecules for all others to use as nutrition.
Organisms that do not rely on those complex biomolecules but can support themselves are called autotroph. So photosynthetic organisms are  photoautotroph and micro organisms that use chemical energy from inorganic compounds are chemoautotroph. The inorganic compounds used can be as simple as decomposed water by radioactive decay.