The influence of rarefaction on heat transfer in circular tubes is studied. A spatial rescaling factor rho(s), which is a measure of rarefaction through its dependence on the Knudsen number, is introduced to identify similarities with the classical Graetz problem. It is found that heat transfer depends both on the degree of rarefaction and on the surface accommodation coefficients. The temperature jump at the wall, ignored in recent investigations, is found to be of essential importance in the heat transfer analysis. A novel uniform asymptotic approximation to high-order eigenfunctions is derived that allows an efficient and accurate determination of the region close to the entrance.