  A boundary value problem, which could represent a transcendent temperature
conduction problem with evaporation in a part of the boundary, was studied to
determine unknown thermophysical parameters, which can be constants or time
dependent functions. The goal of this paper was elucidate which parameters may
be determined using only the measured superficial temperature in part of the
boundary of the domain. We formulated a nonlinear inverse problem to determine
the unknown parameters and a sensitivity analysis was also performed. In
particular, we introduced a new way of computing a sensitivity analysis of a
parameter which is variable in time. We applied the proposed method to model
tissue temperature changes under transient conditions in a biological problem:
the hamster cheek pouch. In this case, the time dependent unknown parameter can
be associated to the loss of heat due to water evaporation at the superficial
layer of the pouch. Finally, we performed the sensitivity analysis to determine
the most sensible parameters to variations of the superficial experimental data
in the hamster cheek pouch.
