Spin transport by itinerant electrons and collective excitations of localized spins with small relaxation rates is of eminent interest for both fundamental research and applications. Spin-orbit coupling (SOC) is not only considered a crucial origin for spin relaxation in spin transport, it recently emerged as the source of novel quantum phases such as topological insulators or SOC-induced Mott insulators with Jeff = 1/2 pseudospins. Here we show that emergent pseudospin excitations in Sr2IrO4 give rise to significant heat transport despite this compound being a strong SOC-induced Mott insulator. The analysis of the heat conductivity reveals boundary-limited relaxation of the pseudospin excitations at low temperature. However, the relaxation rate dramatically increases upon heating towards room temperature due to thermally activated scattering off phonons. The comparison of this result with findings for cuprate analogs with S = 1/2 spin excitations suggests a radically stronger coupling of the Jeff = 1/2 pseudospin excitations to the lattice.