Monte Carlo simulations for model polymer chains composed of hard spheres with square-well attractions were performed to find a precise relation between the parameters of a crossover theory and the parameters of the square-well chain. For sufficiently large bond lengths, there was a direct relation between the effective parameters of the crossover theory and the second- and third-virial coefficients of the square-well atoms. For the systems under study, the theta temperature is close to the Boyle temperature of the disconnected monomers, is mainly dependent on the details of the monomer-monomer interactions, and is only weakly dependent on the bond length of the chain. Above the theta temperature, the crossover theory is in good agreement with the simulation data. Near the theta point, the main effect of tricritical corrections is a shift in the critical amplitudes. Other effects are extremely small. The simulation data are consistent with the tricritical crossover theory. However, more precise data are needed to quantitatively test the tricritical crossover theory.