The renormalized expectation value of the stress energy tensor of the conformally invariant massless fields in the Israel--Hartle--Hawking state in the Schwarzschild spacetime is constructed. It is achieved through solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric. Specifically, the relation of the results of the present approach to the stress tensor constructed within the framework of the Hadamard renormalization is analysed. Finally, the semi-analytic models reconstructing the numerical estimates of the tangential component of the stress-energy tensor with the maximal deviation not exceeding 0.7 % are constructed.

PACS numbers: 04.62.+v, 04.70.Dy