As global studies of climate change depict increasingly dire outcomes of extreme heat, there is an urgent need to understand the appropriateness of heatwave definitions and temperature datasets in different parts of the world. We carry out an intercomparison of the CHIRTS gridded station-satellite temperature dataset with three reanalysis products, ERA5, NCEP-DOE Reanalysis 2, and MERRA2, to assess biases in the absolute value of extreme heat events and the distribution of extreme events. We find close agreement between all four datasets in the magnitude and distribution of extreme temperatures, with a cold bias in the reanalyses over mountainous areas. However, there is little to no agreement between datasets on the timing of extreme heat events in the tropics, and the datasets do not even agree on which month is the hottest month climatologically in these regions. Second, we compare how the four datasets represent the frequency and timing of extreme heat events, using two different types of heatwave definitions: 5-day duration-based extremes and extreme temperature-humidity combinations (heat index). In the case of 5-day heatwaves, there are almost zero events recorded historically in tropical regions. In contrast, high absolute values of the heat index are most common in dry climates, likely due to the dominance of high temperature spikes in these regions, and high heat index events also occur in temperate and tropical regions. There is little agreement between datasets, however, on when these extreme heat index events have happened historically in the tropics. Given these results, we highlight the need for locally developed heatwave metrics for different parts of the world, and we urge against the use of a single heatwave definition in global studies. We also recommend that any studies assessing heat-health relationships in tropical regions beware of the lack of agreement between observational and reanalysis datasets and compare results from different gridded dataset products to estimate uncertainty in heat-health relationships.