In recent years, new spin-dependent thermal effects have been discovered in ferromagnets, stimulating a growing interest in spin caloritronics, a field that exploits the interaction between spin and heat currents. Amongst the most intriguing phenomena is the spin Seebeck effect, in which a thermal gradient gives rise to spin currents that are detected through the inverse spin Hall effect. Non-magnetic materials such as graphene are also relevant for spin caloritronics, thanks to efficient spin transport, energy-dependent carrier mobility and unique density of states. Here, we propose and demonstrate that a carrier thermal gradient in a graphene lateral spin valve can lead to a large increase of the spin voltage near to the graphene charge neutrality point. Such an increase results from a thermoelectric spin voltage, which is analogous to the voltage in a thermocouple and that can be enhanced by the presence of hot carriers generated by an applied current. These results could prove crucial to drive graphene spintronic devices and, in particular, to sustain pure spin signals with thermal gradients and to tune the remote spin accumulation by varying the spin-injection bias.