  In a two-dimensional Bose-Einstein condensate the reduction in dimensionality
fundamentally influences collisions between the atoms. In the crossover regime
from three to two dimensions several scattering parameters have been
considered. However, finite temperature results are more difficult to obtain.
In this work we present the many-body T-matrix at finite temperatures within a
gapless Hartree-Fock-Bogoliubov approach and compare to zero and finite
temperature results obtained using different approaches. A semi-classical
renormalization method is used to remove the ultra-violet divergence of the
anomalous average.
