  This is an extension of the paper [14] by the author for the 2+1 dimensional
Maxwell-Klein-Gordon equations in temporal gauge to the n+1 dimensional
situation for $n \ge 3$. They are shown to be locally well-posed for low
regularity data, in 3+1 dimensions even below energy level improving a result
by Yuan. Fundamental for the proof is a partial null structure of the
nonlinearity which allows to rely on bilinear estimates in wave-Sobolev spaces,
in 3+1 dimensions proven by d'Ancona, Foschi and Selberg, on an
$(L^{\frac{2(n+1)}{n-1}}_x L^2_t)$ - estimate for the solution of the wave
equation, and on the proof of a related result for the Yang-Mills equations by
Tao.
