  We design quantum refrigerators based on spin-j quantum XYZ and
bilinear-biquadratic models with individual spins attached to bosonic thermal
baths. By considering both local and global master equations, we illustrate an
enhancement in the performance of the refrigerators with an increase in the
spin dimension irrespective of the choice of the spin models. To assess the
performance of the refrigerators, we introduce a distance-based measure to
quantify the local temperature of a particle with arbitrary spin quantum number
j. Interestingly, we find that the local temperature quantifier, defined via
minimizing the distance between a spin-j thermal state and the evolved state of
the spin-j particle in the steady state, coincides with the population-based
definition of local temperature known in the literature for spin-1/2 particles.
Moreover, we demonstrate that the qualitative behavior of the distance-based
local temperature is independent of the choice of the distance measure by
comparing the trace distance, Uhlmann's fidelity and relative entropy distance.
We further observe by computing local master equation that the quantum
refrigerator consisting of a spin-1/2 and a spin-j particle can lead to a lower
local temperature compared to a refrigerator with two identical spin-j
particles following the XYZ interactions.
