By introducing suitable parameters, it is demonstrated that the heat conduction effect resembles an elastic deformation. The difference is that the mechanical stress variation induces an inertia effect, while the heat stress variation generates a diffusion effect. Guided by this resemblance, a compatible Lagrangian formulation and its complementary form are derived for the heat conduction problems. The results are similar to Biot’s variational principles. The advantages of using the complementary form for the approximate solutions are also discussed. Temperature distributions in a semi‐infinite solid with prescribed wall temperatures and with described heat flux are considered as illustrative examples.