This paper presents a thermal analysis of thin-wall pipes under non-uniform heat flux in the circumferential direction, with a turbulent flow in statistically stationary state inside. The temperature distribution in the solid and in the fluid is obtained using an spectral method that solves the conjugate heat transfer problem. Special attention is paid to the film temperatures and the thermal stresses on the solid, that are compared to predictions based on 1D models in which the the circumferential heat transfer is neglected. The comparison shows that, even if at sufficiently large Biot numbers (Bi 0.2) the 1D model gives a reasonable prediction of the film temperatures (less than 5% of error), the 1D model for the thermal stresses is only appropriate for very large Biot numbers (Bi 10), giving qualitatively wrong results for Biot numbers below 0.3.