The thermal history of Martian meteorite ALH84001 has critical implications for its petrological and deformational history, the age of its trapped atmospheric gases, the timing of the Martian dynamo, and possibly the evolution of Martian surface temperatures during the last 4 billion years (Gyr). Feldspathic glass in ALH84001 has been dated using 40K/ 40Ar and 40Ar/ 39Ar chronometry by several laboratories. There is general agreement that these chronometers were last reset sometime between 3.9 and 4.3 billion years ago (Ga). Using the 40Ar/ 39Ar data from Bogard and Garrison [Meteorit. Planet. Sci. 34 (1999) 451-473] to model several limiting thermal histories of the meteorite, here we show that most of ALH84001 feldspathic glass has probably not been heated to more than ∼350-500°C and shocked to peak pressures ∼>1 GPa since the glass was last melted. This indicates that most of ALH84001 has been well below these temperatures since 3.9-4.3 Ga. Since these temperatures are below the Curie point of magnetite, much of the magnetization recently identified in ALH84001 carbonate [Weiss et al., Earth Planet. Sci. Lett. this issue] must have been acquired by ∼4 Ga. This also provides an explanation for why ALH84001 contains a sample of an apparently ancient Martian atmosphere that is less evolved relative to that on present-day Mars. Our calculations also suggest that for the last 4 Gyr, average surface temperatures on Mars may not have been much higher than the present cold conditions.