  Fluctuation theorems are fundamental extensions of the second law of
thermodynamics for small nonequilibrium systems. While work and heat are
equally important forms of energy exchange, fluctuation relations have not been
experimentally assessed for the generic situation of simultaneous mechanical
and thermal changes. Thermal driving is indeed generally slow and more
difficult to realize than mechanical driving. We here use feedback cooling
techniques to implement fast and controlled temperature variations of an
underdamped levitated microparticle that are one order of magnitude faster than
the equilibration time. Combining mechanical and thermal control, we verify the
validity of a fluctuation theorem that accounts for both contributions, well
beyond the range of linear response theory. Our system allows the investigation
of general far-from-equilibrium processes in microscopic systems that involve
fast mechanical and thermal changes at the same time.
