To understand why tropical islands are rainier than nearby ocean areas, we explore how a highly idealized island, which differs from the surrounding ocean only in heat capacity, might respond to the diurnal cycle and influence the tropical climate, especially the spatial distribution of rainfall and the thermal structure of the troposphere. We perform simulations of three‐dimensional radiative‐convective equilibrium with the System for Atmospheric Modeling (SAM) cloud‐system‐resolving model, with interactive surface temperature, where a highly idealized, low heat capacity circular island is embedded in a slab‐ocean domain. The calculated precipitation rate over the island can be more than double the domain average value, with island rainfall occurring primarily in an intense, regular thunderstorm system that forms in the afternoon to early evening each day. Island size affects the magnitude of simulated island rainfall enhancement, the intensity of the convection, and the timing of the rainfall maximum relative to solar noon. A combination of dynamic and thermodynamic mechanisms leads to a monotonic enhancement of domain‐averaged tropospheric temperature with increasing fraction of island surface, which may contribute to localization of ascent over the Maritime Continent and its relationship to the Walker Circulation.