  The renormalized expectation value of the stress-energy tensor of the
conformally invariant massless field 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 the 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 tangential component of the stress-energy tensor with the
maximal deviation not exceeding 0.7% are constructed.
