A thermodynamic model of thermoelectric (TE) generator (TEG) driven TE heat pump (TEH) combined-device (TEG-TEH) with Thomson effect and external heat transfer loss is built by using non-equilibrium thermodynamics and finite-time thermodynamics. Heating load, COP and exergetic efficiency are derived and optimized by optimizing distributions of heat conductances among four heat exchangers (HEXs) and TE element numbers between TEG and TEH, respectively, with fixed total number of TE element and fixed HEX inventory. Influences of heat source temperature of TEG, heating space temperature of TEH and Thomson effect on general performances and optimal performances are analyzed. The results show that Thomson effect makes general performances and optimal performances of combined device decrease. Thomson effect makes the maximum COP, maximum heating load and maximum exergetic efficiency decrease from $15.68\times {10}^{-2}$, 28.44 W and 3.651% to $10.27\times {10}^{-2}$, 21.68 W and 2.404%, respectively, makes the optimal performance ranges narrow down, makes the optimal distribution range of TE element numbers between TEH and TEG, optimal distribution range of heat conductances between TEH and TEG, and optimal distribution range of heat conductances between hot- and cold HEXs in TEG narrow down, and makes the optimal distribution range of heat conductances between hot- and cold-side HEXs in TEH broaden.