Spontaneous collapse models assume that quantum systems ungergo slight universal decoherence by some, yet hypothetic, mechanism also leading to spontaneous collapse of the wavefunction. Spontaneous decoherence and collapse are accompanied by tiny spontaneous heating. Such non-quantum bye-product can be the earliest possible test to falsify or confirm the said modifications of standard quantum mechanics. In elementary terms, I outline two leading models, one of which I'm author of. I show that the heating effect of spontaneous wavefunction collapse models implies an experimentally significant increment of equilibrium temperature in massive mechanical oscillators of very slow ring-down time.