We investigate transient spin-dependent thermoelectric signatures in a single-molecule magnet under the effect of a time-dependent voltage pulse. We model the system using nonequilibrium Green's functions and a generalized spin equation of motion incorporating the dynamic electronic structure of the molecule. We show that the generated heat current in the system is due to both charge and spin contributions, related to the Peltier and the spin-dependent Peltier effect. There is also a clear signature in the heat current due to the spin dynamics of the single molecule and a possibility to control the spin-dependent heat currents by bias, tunneling coupling, and exchange interaction. A reversal of the net heat transfer in the molecule is found for increasing bias voltage due to the local Zeeman split and we can correlate the net heat transfer with the local anisotropies and dynamic exchange fields in the system.