We present an analysis of the thermodynamics of the coil-to-globule transition of a beadspring heteropolymer in selective solvent conditions in confined geometries. We have used the continuous-space version of the Wang-Landau Monte Carlo simulation algorithm. Generally, decreasing volume of confinement stabilizes the compact state, reflected directly by an increase in the transition temperature, in agreement with previous theoretical pictures. We propose a new scaling relationship for the shift in the transition temperature in which the changes in latent heat and latent entropies upon confinement scale with the confining geometry size with slightly different scaling exponents. The model agrees with the simulation data well and slightly outperforms simpler scaling models used in the past. Details of the algorithm, including novel trial moves, are presented and discussed. In particular, we find it useful to use so-called "partial molecular dynamics" trial moves.