The T_c -mapping method using low temperature scanning electron microscopy (LTSEM) has been developed to study the spatial distribution of the critical temperature in HTSC films with a spatial resolution approaching 2 microns. To achieve so high a spatial resolution, a numerical deconvolution method was applied that eliminated distorting effects associated with the thermal diffusion and with the contribution from the absorbed beam current. The T_c-mapping method was used to investigate modification by water of YBa₂Cu₃O₇ films grown on (100) MgO and (110) LaAlO₃ substrates. The rate of modification of a [110]-oriented YBa₂Cu₃O₇/LaAlO₃ film is found to be 40 times that of a c-axis oriented YBa₂Cu₃O₇/MgO epitaxial film. It is argued that water-initiated modification of the films results from penetration of hydrogen into the films, rather than from outdiffusion of oxygen.