We use a numerical model to investigate the factors that control the presence or absence of a hot crater lake at an active volcano. We find that given a suitable pair of parameters (e.g., the enthalpy of subaqueous fumaroles and the ratio of mass flux of the fluid input at the lake bottom to lake surface area), hot crater lakes can be sustained on relatively long timescales. Neither a high rate of precipitation nor an impermeable layer beneath the lake bottom are always necessary for long‐term sustainability. The two controlling parameters affect various hydrological properties of crater lakes, including temperature, chemical concentrations, and temporal variations in water levels. In the case of low‐temperature crater lakes, increases in flux and enthalpy, which are a common precursor to phreatic or phreatomagmatic eruptions, result in an increase in both temperature and water level. In contrast, a decrease in water level accompanied by a rise in temperature occurs at high‐temperature lakes. Furthermore, our model suggests that crater geometry is a key control on water temperature. For lakes with a conical topography, a perturbation in the water level due to trivial nonvolcanic activity, such as low levels of precipitation, can cause persistent increases in water temperature and chemical concentrations, and a decrease in the water level, even though subaqueous fumarolic activity does not change. Such changes in hot crater lakes which are not caused by changes in volcanic activity resemble the volcanic unrest that precedes eruptions.