  We explore proximity-induced magnetocaloric effect (MCE) on transition metal
dichalcogenides, focusing on a two-dimensional (2D) MoTe$_2$ monolayer
deposited on a ferromagnetic semiconductor EuO substrate connected to a heat
source. We model this heterostructure using a tight-binding model,
incorporating exchange and Rashba fields induced by proximity to EuO, and
including temperature through Fermi statistics. The MCE is induced on the 2D
MoTe$_2$ layer due to the EuO substrate, revealing large spin-polarized entropy
changes for energies out of the band gap of the MoTe$_2$-EuO system. By gating
the chemical potential, the MCE can be tuned to produce heating for spin up and
cooling for spin down across the $K$ and $K'$ valley splitting in the valence
band, whereas either heats or cools for both spins in the conduction band. The
Rashba field enhances the MCE in the valence zone while decreasing it in the
conduction bands. The exchange field-induced MCE could be useful to produce
tunable spin-polarized thermal responses in magnetic proximitized 2D materials.
