  In this paper, we present first-order accurate numerical methods for solution
of the heat equation with uncertain temperature-dependent thermal conductivity.
Each algorithm yields a shared coefficient matrix for the ensemble set
improving computational efficiency. Both mixed and Robin-type boundary
conditions are treated. In contrast with alternative, related methodologies,
stability and convergence are unconditional. In particular, we prove
unconditional, energy stability and optimal-order error estimates. A battery of
numerical tests are presented to illustrate both the theory and application of
these algorithms.
