  We construct and study the approximate stress-energy tensor of the quantized
massive scalar field in higher dimensional Schwarzschild-Tangherlini
spacetimes. The stress-energy tensor is calculated within the framework of the
Schwinger-DeWitt approach. It is shown that in $N$-dimensional spacetime the
main approximation can be obtained from the effective action constructed form
the coincidence limit of the Hadamard-DeWitt coefficient $a_{k},$ where $k-1$
is the integer part of $N/2$. The back reaction of the quantized field upon the
black hole spacetime is analyzed and the quantum-corrected Komar mass and the
Hawking temperature is calculated. It is shown that for the minimal and
conformal coupling the increase of the Komar mass of the quantum corrected
black hole leads to the decrease of its Hawking temperature. This is not
generally true for more exotic values of the coupling parameter. The general
formula describing the vacuum polarization, $ \langle \phi^{2} \rangle,$ is
constructed and briefly examined.
