  We study conversion of thermal energy to mechanical energy and vice versa in
$\alpha$-Fermi-Pasta-Ulam-Tsingou~(FPUT) chain with spatially sinusoidal
profile of initial temperature. We show analytically that coupling between
macroscopic dynamics and quasiballistic heat transport gives rise to mechanical
vibrations with growing amplitude. This new phenomenon is referred to as
"ballistic resonance". At large times, these mechanical vibrations decay
monotonically, and therefore the well-known FPUT recurrence paradox occurring
at zero temperature is eliminated at finite temperatures.
