We propose a method that makes use of the nonlinear properties of some hypothetical microscopic solid material as the working substance for a microscopic machine. The protocols used are simple (step and elliptic) and allow us to obtain the work and heat exchanged between machine and reservoirs. We calculate the work for a nonlinear single-particle machine that can be treated perturbingly. We obtain the instantaneous work and heat for the machine undergoing cycles that mimic the Carnot and multireservoir protocols. The work calculations are then extended to high values of the nonlinear parameter yielding the quasistatic limit, which is verified numerically. The model we propose is fluctuation driven and we can study in detail its thermostatistics, namely, the work distribution both per cycle and instantaneous and the corresponding fluctuation relations.