We present the theory of the longitudinal spin Seebeck effect between a Heisenberg spin-1/2 chain and a conductor. The effect consists of the generation of a spin current across the spin chain-conductor interface in response to the temperature difference between the two systems. In this setup, the current is given by the convolution of the local spin susceptibilities of the spin chain and the conductor. We find the spin current to be fully controlled, both in the magnitude and the sign, by the backscattering interaction between spinons, fractionalized spin excitations of the Heisenberg chain. In particular, it vanishes when the spinons form a non-interacting spinon gas. Our analytical results for the local spin susceptibility at the open end of the spin chain are in excellent agreement with numerical DMRG simulations.