  Superconducting spintronics is based on the creation of spin-triplet Cooper
pairs in ferromagnet-superconductor (F-S) hybrid junctions. Previous proposals
to manipulate spin-polarized supercurrents on-demand typically require the
ability to carefully control magnetic materials. We, instead, propose a quantum
heat engine that generates equal-spin Cooper pairs and drives supercurrents
on-demand without manipulating magnetic components. We consider a S-F-S
junction, connecting two leads at different temperatures, on top of the helical
edge of a two-dimensional topological insulator. Heat and charge currents
generated by the thermal bias are caused by different transport processes,
where electron cotunneling is responsible for the heat flow to the cold lead
and, strikingly, only crossed Andreev reflections contribute to the charge
current. Such a purely nonlocal Andreev thermoelectric effect injects
spin-polarized Cooper pairs at the superconductors, generating a supercurrent
that can be switched on/off by tuning their relative phase. We further
demonstrate that signatures of spin-triplet pairing are facilitated by rather
low fluctuations of the thermoelectric current for temperature gradients
smaller than the superconducting gap.
