  We show that the heating effect of spontaneous wave-function collapse models
implies an experimentally significant increment $\Delta T$ of equilibrium
temperature in a mechanical oscillator. The obtained form $\Delta T$ is linear
in the oscillator's relaxation time $\tau$ and independent of the mass. The
oscillator can be in a classical thermal state, the effect $\Delta T$ is
classical for a wide range of frequencies and quality factors. We note that the
test of $\Delta T$ does not necessitate quantum state monitoring but
tomography. In both gravity-related (DP) and continuous spontaneous
localization (CSL) models the strong-effect edge of their parameter range can
be challenged in existing experiments on classical oscillators. For the CSL
theory, the conjectured highest collapse rate parameter values become
immediately constrained by evidences from current experiments on extreme
slow-ring-down oscillators.
