Extreme heat can cause great harm to crop production, but this effect is not always included in global land surface models. In this study, new functions are introduced in the Community Land Model v5 (CLM5) to account for heat stress effects induced by heatwaves (3 days) that can result in crop yield losses by looking at vegetation temperature and a regionally-varying temperature trigger on a global scale. Two different heat stress implementations are tested, both targeted to affect the reproductive stage of the growing season. In the first method, heat stress accelerates senescence of Leaf Area Index (LAI), and in the second, heat stress directly reduces carbon allocation to grains for yield. The resulting impact on yield for the different experiments is then evaluated for the crops wheat, maize, rice and soybean for the years 1985-2014. We show the added value of using vegetation temperature to distinguish effects between irrigated and rainfed crops. In addition, we highlight the need for using critical thresholds that are not static over the globe, but take into account the regional climate. Both methods capture heat stress during specific events, but since the heat stress implementations  only affect the reproductive crop stage, the potential of an evaluation with reference data becomes limited as the exact timing of the simulated growing season becomes another crucial modeling factor. Comparing the two different implementation methods, the heat stress impact on accelerated LAI senescence had a larger impact in the tropics and subtropics, whereas reducing the carbon allocation to grains for yield had a stronger impact in higher latitudes. The findings of this study advance crop sensitivity to climatic heat extremes in global land surface models.