The thermal dynamics and transient optical response of individual gold nanodisks supported on thin silicon nitride membranes were investigated using optical time-resolved pump-probe spectroscopy and finite-element modeling. The effect of reducing the membrane thickness from 50 nm to 15 nm on the nanodisk thermal dynamics was explored. A significant deceleration of the nanodisk cooling kinetics was observed, and linked to a quasi-two-dimensional heat diffusion process within the 15 nm thick membrane, without detectable modification of its thermal conductivity. Systematic measurements involving different optical probe wavelengths additionally revealed the contribution of indirect membrane heating to the measured time-resolved signals, an effect particularly pronounced in the spectral range where direct optical heating of the nanodisk induces minimal ultrafast modifications of its extinction cross-section.