Shock heating of the Dhofar 378 (Dho 378) Martian shergottite produced melting, vesiculation, and flow of the plagioclase, which upon cooling recrystallized into complex textures. Heating experiments on the similar Zagami shergottite indicate that Dho 378 was shock heated to 1000-1100°C and was cooled at ~2.5°C/h. An 39Ar-40Ar analysis of Dho 378 plagioclase indicates different Ar diffusion domains and K/Ca ratios. The lower-temperature phase defines an Ar-Ar isochron age of 141 +/- 32 Ma. The higher-temperature phase released more 40Ar but does not define an age. The meteorite's thermal history was examined by constructing a generic model to compare cooling rates for objects of different sizes against fractional diffusion loss of Ar for different cooling times. Using gas diffusion parameter values measured for Dho 378, this model indicates that it is improbable that the major shock heating event occurred at the time that Dho 378 was ejected from Mars ~3 Ma ago. Rather, we suggest that the time of shock heating is probably given by its Ar-Ar age. For Dho 378 to cool sufficiently fast not to lose most of its 40Ar ~3 Ma ago would require it to have been ejected into space as an impossibly small object. Larger and more reasonable Mars ejection sizes indicate that Dho 378 should have lost most of its 40Ar. On the basis of plagioclase texture and Ar data, we suggest that a major impact event ~141 Ma ago melted Dho 378 plagioclase, degassed most of its 40Ar, and deposited it in crater ejecta to cool. A smaller and later impact ejected it into space ~3 Ma ago.