Gold nanoparticles are well-known to exhibit size-dependent properties that are responsible for their unique catalytic, optical, and electronic applications. However, electron-phonon coupling, which is important for photocatalysis and light harvesting, is one of the rare properties of gold that is size-independent above a threshold value, e.g., for nanospheres larger than approximately 5 nm in diameter. Here, we show that when interfaced to a comparably sized Pt nanoparticle, the electron-phonon coupling constant of the hybrid material depends on the diameter of the Au domain. This is important because the electron-phonon coupling constant describes the efficiency by which hot electrons are converted to local heat by the primary electron-phonon scattering thermalization channel. We begin by synthesizing a library of Au-Pt hybrid nanoparticle heterodimers by growing size-tunable Au nanoparticles on Pt nanoparticle seeds. By systematically varying reagent concentration and reaction time, the Au domain diameter of the Au-Pt hybrid nanoparticle heterodimers can be tuned between 4.4 and 16 nm while the size of the Pt domain remains constant. Calibration curves allow us to dial in precise Au domain sizes, and microscopic analysis of the Au-Pt heterodimers provides insights into how they grow and how their morphologies evolve. Femtosecond time-resolved transient absorption spectroscopy reveals that for Au-Pt heterodimers having Au domain diameters of 8.7 to 14 nm, the electron-phonon coupling constant decreases by more than 80%, which is not observed for comparably sized Au nanoparticles. Interfacing smaller Au domains with Pt nanoparticle surfaces causes an increase in the density of states near the Fermi level of Au, which results in accelerated thermalization times through an increased number of electron-phonon interactions. The combination of precision hybrid nanoparticle synthesis and size-dependent electron-phonon coupling may be important for designing composite metals for photocatalytic and light-harvesting applications and for engineering different functions into established materials.