We show that any generic nonadiabatic slow flow of ideal compressible fluid develops a significant vorticity. As an example, an initially irrotational conductive cooling flow (CF) is considered. A perturbation theory for the vorticity generation is developed that employs, as a zero order solution, a novel two-dimensional similarity solution. Full gasdynamic simulations of this CF demonstrate the vorticity generation and support the theory. The relevance of this problem to the experiments with the “hot channels” is discussed.