  (Abridged) We present a multi-epoch spectral study of the Transient Anomalous
X-ray Pulsar XTE J1810-197 obtained with the XMM X-ray telescope. Four
observations taken over the course of a year reveal strong spectral evolution
as the source fades from outburst. The origin of this is traced to the
individual decay rates of the pulsar's spectral components. A 2-T fit at each
epoch requires nearly constant temperatures of kT=0.25 & 0.67 keV while the
component luminosities decrease exponentially with tau=900 & 300d,
respectively. One possible interpretation is that the slowly decaying cooler
component is the radiation from a deep heating event that affected a large
fraction of the crust, while the hotter component is powered by external
surface heating at the foot-points of twisted magnetic field lines, by
magnetospheric currents that are decaying more rapidly. The energy-dependent
pulse profile of XTE J1810-197 is well modeled at all epochs by the sum of a
sine and triangle function. These profiles peak at the same phase, suggesting a
concentric surface emission geometry. The spectral and pulse evolution together
argue against the presence of a significant ``power-law'' contribution to the
X-ray spectrum below 8 keV. The extrapolated flux is projected to return to the
historic quiescent level, characterized by an even cooler blackbody spectrum,
by the year 2007.
