You might expect tempers to boil over and violence to spike in a heatwave. You might also expect heat to make people lethargic and less likely to exert themselves. Crime statistics show that both effects are real.
In Britain, we spend more time outside in summer, and the whole pattern of crime changes, so it is not just a matter of warmth. However, statistical studies in many countries, comparing warmer years with cooler ones, strongly suggest that temperature affects violence.
A study in New South Wales found that the number of cases of assault each day rose as it got hotter, but dropped when the temperatures passed 30C. Non-violent crimes, such as fraud, did not increase the same way.
Researchers in Korea found a direct association between temperature and assault, while in Finland violent crime appears to rise by about 2% per degree temperature increase. In Chicago, an analysis of 5m police reports since 2001 shows a steady increase of crime rate with temperatures up to 32C, but falling off after that.
The reasons behind these effects have not been fully studied, but the intuitive explanation may be the best one. High temperatures make people more impulsive, and violent acts get committed literally in the heat of the moment.