We study two reciprocal thermal effects in the ferromagnetic semiconductor (Ga, Mn)As by scattering theory: domain wall motion induced by a temperature gradient and heat currents pumped by a moving domain wall. The effective out-of-plane thermal spin transfer torque parameter PQ βQ, which governs the coupling between heat currents and a magnetic texture, is found to be of the order of unity. Unpinned domain walls are predicted to move at speed 10 m/s in temperature gradients of the order 10 K/μm. The cooling power of a moving domain wall only compensates the heating due to friction losses at ultra-low domain wall velocities of about 0.07 m/s. The Seebeck coefficient is found to be of the order 100-500 μV/K at T = 10 K, in good agreement with recent experiments.