  This paper investigates the numerical modeling of a time-dependent heat
transmission problem by the convolution quadrature boundary element method. It
introduces the latest theoretical development into the error analysis of the
numerical scheme. Semigroup theory is applied to obtain stability in spatial
semidiscrete scheme. Functional calculus is employed to yield convergence in
the fully discrete scheme. In comparison to the traditional Laplace domain
approach, we show our approach gives better estimates.
