  The approximate renormalized stress-energy tensor of the quantized massive
conformally coupled scalar field in the spacetime of electrically charged
nonlinear black hole is constructed. It is achieved by functional
differentiation of the lowest order of the DeWitt-Schwinger effective action
involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely
coefficient $a_{3}.$ The result is compared with the analogous result derived
for the Reissner-Nordstr\"om black hole. It is shown that the most important
differences occur in the vicinity of the event horizon of the black hole near
the extremality limit. The structure of the nonlinear black hole is briefly
studied by means of the Lambert functions.
