We explain how the phenomena of ferroelectric phase transition temperature ${T}_{c}$ enhancement beyond the end members in perovskite solid solution such as $\mathrm{Bi}M{\mathrm{O}}_{3}\text{\ensuremath{-}}{\mathrm{PbTiO}}_{3}$ ($M=\mathrm{Sc}$, In, etc.) is related to nonlinear and spatial correlation effects. The explanation is based on the calculation of ${T}_{c}$ in the framework of our random field theory with additional account for nonlinear effects in the above substances. We show that the maximum of ${T}_{c}$ for certain ${\mathrm{PbTiO}}_{3}$ content takes place when coefficient of nonlinearity is positive, the value of this coefficient is found from best fit between theory and experiment. This nonlinearity coefficient is the only adjustable parameter of the theory. We show that enhancement of positive nonlinearity coefficients enhances greatly the ${T}_{c}$ maximum over its value for end members.The theory lays the foundation to calculate not only ${T}_{c}$ for above solid solutions but virtually any equilibrium and/or nonequilibrium thermodynamic characteristics such as static and dynamic dielectric susceptibility, specific heat, etc., as a function of ${\mathrm{PbTiO}}_{3}$ content, temperature, electric field, and other external parameters.