We present a study of the thermal conductivity k and the thermopower S of single crystals of La_{1-x}Sr_xCoO_3 with 0<= x <= 0.3. For all Sr concentrations La_{1-x}Sr_xCoO_3 has rather low k values, whereas S strongly changes as a function of x. We discuss the influence of the temperature- and the doping-induced spin-state transitions of the Co ions on both, S and k. From S, k, and the electrical resistivity rho we derive the thermoelectric figure of merit Z=S^2/(k*rho). For intermediate Sr concentrations we find notably large values of Z indicating that Co-based materials could be promising candidates for thermoelectric cooling.