  We introduce a solvable system of equations that describes non-extremal
multicenter solutions to six-dimensional ungauged supergravity coupled to
tensor multiplets. The system involves a set of functions on a
three-dimensional base metric. We obtain a family of non-extremal axisymmetric
solutions that generalize the known multicenter extremal solutions, using a
particular base metric that introduces a bolt. We analyze the conditions for
regularity, and in doing so we show that this family does not include solutions
that contain an extremal black hole and a smooth bolt. We determine the
constraints that are necessary to obtain smooth horizonless solutions involving
a bolt and an arbitrary number of Gibbons-Hawking centers.
