  We study the effects of the time-variable properties of thermonuclear X-ray
bursts on modeling their millisecond-period burst oscillations. We apply the
pulse profile modeling technique that is being used in the analysis of
rotation-powered millisecond pulsars by the Neutron Star Interior Composition
Explorer (NICER) to infer masses, radii, and geometric parameters of neutron
stars. By simulating and analyzing a large set of models, we show that
overlooking burst time-scale variability in temperatures and sizes of the hot
emitting regions can result in substantial bias in the inferred mass and
radius. To adequately infer neutron star properties, it is essential to develop
a model for the time variable properties or invest a substantial amount of
computational time in segmenting the data into non-varying pieces. We discuss
prospects for constraints from proposed future X-ray telescopes.
