  Based on a time-dependent Ginzburg-Landau system of equations and finite
element modeling, we present novel results related with the physics of
phase-slippage in superconducting wires surrounded by a non-superconductive
environment. These results are obtained within our previously reported approach
related to superconducting rings and superconductive gravitational wave
detector transducers. It is shown that the phase-slip centers (PSCs) can be
effective in originating not only positive but also negative thermal fluxes.
With an appropriate design utilizing thermal diodes, PSCs can serve as
cryocooling engines. Operating at $T\sim 1$ K cryostat cold-finger, they can
achieve sub-Kelvin temperatures without using $^3$He.
