The metabolic theory of ecology (MTE) provides a general framework of allometric and thermal dependence that may be useful for predicting how climate change will affect disease spread. Using Daphnia magna and a microsporidian gut parasite, we conducted two experiments across a wide thermal range and fitted transmission models that utilize MTE submodels for transmission parameters. We decomposed transmission into contact rate and probability of infection, and further decomposed probability of infection into a product of gut residence time (GRT) and per-parasite infection rate of gut cells. Contact rate generally increased with temperature and scaled positively with body size, whereas infection rate had a narrow hump-shaped thermal response and scaled negatively with body size. GRT increased with host size and was longest at extreme temperatures. GRT and infection rate inside the gut combined to create a 3.5x higher probability of infection for the smallest relative to the largest individuals. Small temperature changes caused large differences in transmission. We also fit several alternative transmission models to data at individual temperatures. The more complex models, parasite antagonism or synergism and host heterogeneity, did not substantially improve the fit to the data. Our results show that transmission rate is the product of several distinct thermal and allometric functions that can be predicted continuously across temperature and host size using MTE.