The solid of revolution were under operating of appended axisymmetric surface forces and a non-steady thermal field is esteemed. With the help of a method of biharmonic potentials is instituted tight and strained state of this body with usage of cylindrical axials. The solution of a problem of thermoelasticity is reduced to a solution of some elastic problem at operating padding mass and surface forces originating at the expense of irregular heating (chilling). The algorithm of a numerical solution is designed. The fidelity of algorithm is affirmed by a solution of problem problems.