  Pulse profile modelling (PPM) is a comprehensive relativistic ray-tracing
technique employed to determine the properties of neutron stars. In this study,
we apply this technique to the Type I X-ray burster and accretion-powered
millisecond pulsar XTE J1814-338, extracting its fundamental properties using
PPM of its thermonuclear burst oscillations. Using data from its 2003 outburst,
and a single uniform temperature hot spot model, we infer XTE J1814-338 to be
located at a distance of $7.2^{+0.3}_{-0.4}$ kpc, with a mass of
$1.21^{+0.05}_{-0.05}$ M$_\odot$ and an equatorial radius of
$7.0^{+0.4}_{-0.4}$ km. Our results also offer insight into the time evolution
of the hot spot but point to some potential shortcomings of the single uniform
temperature hot spot model. We explore the implications of this result,
including what we can learn about thermonuclear burst oscillation mechanisms
and the importance of modelling the accretion contribution to the emission
during the burst.
