Abstract: The solution of the heat balance equation for gas-cooled current leads is presented. In the process of searching for the final solution, the functional relation of the dependent parameter to the independent parameters must be obtained first. Then, the domains of definition for the parametric equations should be turned to the form containing only independent variables, instead of that including dependent variables as well as independent variables. Moreover, in the existential range of the all solutions for the parametric equations, the part in which the trivial solutions exist should be determined and excluded from consideration. Only whenroblems are given and discussed.