Due to short test time, heat conduction was considered as transient in hypersonic shock tunnels. The heat flux measurement and data processing were operated basing on one-dimensional semi-infinite heat conduction theory. However, for models with local large curvature or small radius, it resulted in significant compression or expansion of space for heat transfer, or lateral heat conduction, which made the hypothesis of one-dimensional unsatisfied and errors. In this paper, approximate solutions for the unsteady heat conduction in cylindrically convex and concave shells were established, and were used for further analysis of the errors, with forms of heating load, location and curvature radius of heated surface taken into consideration. (C) 2022 Elsevier Ltd. All rights reserved.