We report on photo-thermal modulation of thin film surface plasmon polaritons (SPP) excited at telecom wavelengths and traveling at a gold/air interface. By operating a modulated continuous-wave or a Q-switched nanosecond pump laser, we investigate the photo-thermally induced modulation of SPP propagation mediated by the temperature-dependent ohmic losses in the gold film. We use a fiber-to-fiber characterization set-up to measure accurately the modulation depth of the SPP signal under photo-thermal excitation. On the basis of these measurements, we extract the thermo-plasmonic coefficient of the SPP mode defined as the temperature derivative of the SPP damping constant. Next, we introduce a figure of merit which is relevant to characterize the impact of temperature onto the properties of bounded or weakly leaky SPP modes supported by a given metal at a given wavelength. By combining our measurements with tabulated values of the temperature-dependent imaginary part of gold dielectric function, we compute the thermo-optical coefficients (TOC) of gold at telecom wavelengths. Finally, we investigate a pulsed photo-thermal excitation of the SPP in the nanosecond regime. The experimental SPP depth of modulation obtained in this situation are found to be in fair agreement with the modulation depths computed by using our values of gold TOC.