  We obtain and study static, spherically symmetric solutions for the Einstein
- generalized Maxwell field system in 2n dimensions, with possible inclusion of
a massless scalar field. The generalization preserves the conformal invariance
of the Maxwell field in higher dimensions. Almost all solutions exhibit naked
singularities, but there are some classes of black-hole solutions. For these
cases the Hawking temperature is found and its charge/mass and dimension
dependence is discussed. It is shown that, unlike the previously known
multidimensional black-hole solutions, in our case the Hawking temperature may
infinitely grow in the extreme case (that of minimum mass for given charges).
