  The thermoelectric performance of a topological Josephson nonlocal heat
engine is thoroughly investigated. The nonlocal response is obtained by using a
normal metal probe coupled with only one of the proximized helical edges in the
middle of the junction. In this configuration, we investigate how the flux bias
and the phase bias trigger the nonlocal thermoelectric effects under the
application of a thermal difference between the superconducting terminals.
Possible experimental nonidealities such as asymmetric proximized
superconducting gaps are considered showing how the nonlocal response can be
affected. The interplay between Doppler-shift, which tends to close gaps, and
Andreev interferometry, which affects particle-hole resonant transport, are
clearly identified for different operating regimes. Finally, we discuss the
power and the efficiency of the topological thermoelectric engine which reaches
maximum power at maximal efficiency for a well coupled normal probe. We find
quite high nonlocal Seebeck coefficient of the order of tenths of $\mu$V/K at a
few kelvin, a signal that would be clearly detectable also against any spurious
local effect even with moderate asymmetry of the gaps.
