The free motion of a blunted body of revolution of considerable length through a large-scale cloud of heated gas (a thermal) floating in a stratified atmosphere is investigated. An effective numerical method of determining the trajectory of the body is proposed, based on the simultaneous solution of flow and ballistics problems. The flow problem is solved by a numerical method that is very economical in computer time, based on an expansion in a small parameter [1, 2], which is the angle of attack, in conjunction with the global-iteration method [2, 3]. The effect of the floating large-scale cloud of heated gas on trajectory, spatial orientation and stability of the body is determined. It is shown that under certain flight conditions the presence of a floating cloud of reduced density along the path of the body may lead to flipping of the body.