The temporal evolution of past martian surface temperatures is poorly known. We used thermochronology and published noble gas and petrographic data to constrain the temperature histories of the nakhlites and martian meteorite ALH84001. We found that the nakhlites have not been heated to more than 350 degrees C since they formed. Our calculations also suggest that for most of the past 4 billion years, ambient near-surface temperatures on Mars are unlikely to have been much higher than the present cold (<0 degrees C) state.