  Motivated by applications to 3D printing, this paper presents two algorithms
for calculating an ensemble of solutions to heat conduction problems. The
ensemble average is the most likely temperature distribution and its variance
gives an estimate of prediction reliability. Solutions are calculated by
solving a linear system, involving a shared coefficient matrix, for multiple
right-hand sides at each timestep. Storage requirements and computational costs
to solve the system are thereby reduced. Stability and convergence of the
method are proven under a condition involving the ratio between fluctuations of
the thermal conductivity and the mean. A series of numerical tests are provided
which confirm the theoretical analyses and illustrate uses of ensemble
simulations.
