A Temperature-and-Density-Scaling Monte Carlo (TDSMC) study of the square-well fluid was carried out. The relative excess free energy was obtained directly from the simulations with a standard deviation less then 0.5%. Energy, pressure, compressibility and heat capacity were calculated from the excess free energy data. For the system of 256 particles a reduced density interval of 0.1-0.68 and a reduced temperature interval of 1.053-1.29 was covered. In the simulations a "zoom focus" on the temperature-density grid was used: a "panoramic view" of the whole temperature-density region, on a relatively coarse grid, was combined with a "close-up" of the critical-point region, using a finer (T,rho) grid. The coexistence curve was obtained with use of the double-tangent construction on the free energy, and the critical temperature and critical density were estimated. The critical parameters found by the TDSMC method are compared with those of other Monte-Carlo techniques.