Heat waves and wildfires are two natural hazards that cause substantial socio-economic losses and public health risks. Despite the general consensus that heat waves intensify fires, a critical knowledge gap remains on how likely and how many fires would occur concurrently with heat waves across different climate regions. A better understanding of the fire response to heat waves in the Earth system may become increasingly important in the coming decades as the human-caused climate warming persistently increases the frequency, intensity, and duration of temperature extremes. In this presentation, we quantify the sensitivity of global fire number, final fire size, and burned area to heat waves during 2003-2018. By combining individual fire data from the global Fire Atlas with climate observations, we show that two-thirds of global climate regions have experienced an increase in fire number and burned area when heat waves occur during the fire season, with amplification by a factor of up to 5.6 in Northwest of North America. Such heat wave amplification of fires is more consistent in boreal regions and larger in forest ecosystems. By tracking fire dynamics with heat wave duration, we find the burned area is primarily driven by increasing fire ignitions when the heat wave is longer, which is consistent across different latitudes. These results quantitatively reveal the biome-level difference in the fire response to heat waves, which highlights the multiplicative risks of compounding hazards to public health in a warmer future.