In the paper nonlinear direct and inverse transient heat conduction problems are considered.The nonlinearity has been treated by Kirchhoff transformation.Obtained linear problem has been solved by means of Trefftz functions.In this case there are heat polynomials.The solution has been obtained globally in entire time space domain and by means of different variants of Finite Element Method with Trefftz base function(FEMT).Three variants of FEMT are used: continuous(classical FEM with Trefftz base functions),non-continuous(Trefftz base functions without continuity in nodes)and substructuring(nodeless FEMT).The sensitiveness of the method according to data disturbance has been checked.This approach allows to solve direct and inverse heat conduction problems as well.