As long as the first and second laws of thermodynamics are satisfied, then it would be possible in theory. This is a rather vague answer, but the organism would not be able to "live" if it just sat in an environment with a constant temperature. It might be able to go into dormancy in such a case, but dynamic activity would cease.
The organism will only absorb thermal energy if it's cooler than its local environment. Much of this absorbed energy will raise the temperature of the organism, and the rest will be used to drive chemical processes or modify the internal structure directly through thermal expansion/contraction. Some of these chemical processes may have an end result in the organism doing work on the environment or even on its own structure, but only if the first and second laws of thermodynamics can both be satisfied. These processes will stop when the organism reaches thermal equilibrium with its environment. In order to prevent the organism from eventually "cooking", it cannot just keep going warmer environments. It will have to eventually find itself in a local environment that's cooler than it is itself so that it can shed thermal energy, perhaps with the performance of more work. In order to meet any reasonable definition of life, the organism will have to find itself in an environment that oscillates thermally in order for it to create the structures and behaviors we would normally associate with life.
Unless the work the organism does is used to transport itself back and forth between warmer and cooler environments, it will have to rely on an external cause for the thermal oscillations.