In this paper we consider a heat flow in an inhomogeneous. body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.