We analyze theoretically the quantization of conductance occurring with cold atoms trapped in two reservoirs connected by a constriction within which an attractive gate potential is added. We show that the Bose statistics strongly enhances the effect compared to fermions. We focus on temperatures slightly above the condensation threshold in the reservoirs, which contain a thermal gas. The Bose statistics leads to conductance plateaux whose large values depend on the thermodynamics of the gas in the reservoirs. We highlight the key role of weak repulsive interactions between the bosons in preventing them from collapsing into the constriction. We also point out the differences in the thermoelectric effects occurring with bosons and fermions in the quantized conductance regime.