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

Novel results obtained by modeling of dynamic processes in superconductors: phase-slip centers as cooling engines