  This three section report can be regarded as an extended appendix to (Bueler,
Brown, and Lingle 2006). First we give the detailed construction of an exact
solution to a standard continuum model of a cold, shallow, and thermocoupled
ice sheet. The construction is by calculation of compensatory accumulation and
heat source functions which make a chosen pair of functions for thickness and
temperature into exact solutions of the coupled system. The solution we
construct here is ``TestG'' in (Bueler and others, 2006) and the steady state
solution ``Test F'' is a special case. In the second section we give a
reference C implementation of these exact solutions. In the last section we
give an error analysis of a finite difference scheme for the temperature
equation in the thermocoupled model. The error analysis gives three results,
first the correct form of the Courant-Friedrichs-Lewy (CFL) condition for
stability of the advection scheme, second an equation for error growth which
contributes to understanding the famous ``spokes'' of (Payne and others, 2000),
and third a convergence theorem under stringent fixed geometry and smoothness
assumptions.
