Heat can cause substantial yield losses in crop production and climate change is increasing the risk of this kind of damage. Weather index insurance can help to reduce the financial losses resulting from heat exposure. This paper introduces crop-specific payout functions based on restricted cubic splines in heat index insurance. The use of restricted cubic splines is a cutting-edge method to reflect empirically estimated temperature effects on crop yields and to estimate temperature-related yield losses. The integration of these temperature effects in payout functions facilitates insurance design and allows hourly temperatures to be used as the underlying index. An empirical analysis is used to assess heat stress effects for a panel of East German winter wheat and winter rapeseed producers, to calibrate insurance contracts accordingly and simulate the resulting risk reducing capacities. We find that the insurance scheme introduced here leads to statistically and economically significant out-of-sample risk reducing capacities for farmers, i.e. risk premiums are reduced by up to approximately 20% at the median, in comparison to the uninsured status and at the actuarially fair premium. Moreover, we highlight that policy-makers can support the cost-efficient provision of market-based weather index insurance by fostering data collection and data provision.