We investigate the effects of temperature on the nonlinear response functions associated with various two-dimensional vibrational spectroscopies. It turns out that the system-bath interaction plays an important role in determining the nature of the temperature-dependencies of the nonlinear response functions and spectra of the two-dimensional vibrational spectroscopy. For a model Hamiltonian, we present exact quantum-mechanical expressions for the nonlinear response functions of two-dimensional vibrational spectroscopies in both the time and frequency domains.