One theory holds that people are more easily agitated in the heat because adrenaline and testosterone levels rise in the warmer temperatures. If higher temperatures were causing greater crime rates, then we should see crime incidences peak when temperatures are at their highest.
A second theory is that more crime is committed when more people gather in public. During the summer, people – including, say, troubled teenagers who might otherwise be in school – spend more time outside, creating more opportunity for interactions of all sorts, including criminal behavior.