A one-dimensional model is constructed to model the time-evolving temperature and humidity in a droplet’s region of influence. Unlike the ordinary differential equations often used to model a cloud’s supersaturation and latent heating, these partial differential equations do not make any assumption about how supersaturation and latent heating relate to the droplet’s radius. Nevertheless, the emergent behavior from the model is as expected from theory: a droplet’s condensation rate adjusts, nearly instantaneously, to a known factor times the product of supersaturation and droplet radius. It is verified, therefore, that a cloud’s rate of latent heating is proportional to the sum of droplet radii, not the sum of their surface areas.