  We construct multi-center solutions for charged, dilatonic, non-extremal
black holes in D=4. When an infinite array of such non-extremal black holes are
aligned periodically along an axis, the configuration becomes independent of
this coordinate, which can therefore be used for Kaluza-Klein compactification.
This generalises the vertical dimensional reduction procedure to include {\it
non-extremal} black holes. We then extend the construction to multi-center
non-extremal $(D-4)$-branes in $D$ dimensions, and discuss their vertical
dimensional reduction.
