We investigate numerically, for the first time, the thermal counterflow of superfluid helium past acylinder by solving with a finite volume method the complete so-called two-fluid model. In agreement withexisting experimental results, we obtain symmetrical eddies both up- and downstream of the obstacle. Thegeneration of these eddies is a complex transient phenomenon that involves the friction of the normal fluidcomponent with the solid walls and the mutual friction between the superfluid and normal components.Implications for flow in a more realistic porous medium are also investigated.