The approximate renormalized stress-energy tensor of the quantized massiveconformally coupled scalar field in the spacetime of electrically chargednonlinear black hole is constructed. It is achieved by functionaldifferentiation of the lowest order of the DeWitt-Schwinger effective actioninvolving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seelycoefficient $a_{3}.$ The result is compared with the analogous result derivedfor the Reissner-Nordstr\"om black hole. It is shown that the most importantdifferences occur in the vicinity of the event horizon of the black hole nearthe extremality limit. The structure of the nonlinear black hole is brieflystudied by means of the Lambert functions.
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