  In this paper we consider a two component scalar field theory, with
noncommutativity in its conjugate momentum space. We quantize such a theory in
a compact space with the help of dressing transformations and we reveal a
significant effect of introducing such noncommutativity as the splitting of the
energy levels of each individual mode that constitutes the whole system. We
further compute the thermal partition function exactly with predicted deformed
dispersion relations from noncommutative theories and compare the results with
usual results. It is found that thermodynamic quantities in noncommutative
models, irrespective of whether the model is more deformed in infrared/UV
region, show deviation from standard results in high temperature region.
