To elucidate the geological evolution of the mesosiderite stony-iron meteorites and their 3.3-3.8 Gy 40Ar-39Ar ages, we have investigated their shock and thermal histories. We have studied shock metamorphism in sixteen mesosiderites and find that none have been shocked to more than 10 GPa (shock stage S1-S2). Three mesosiderites contain a tiny fraction (approximate to 0.1% overall) of mineral fragments that were shocked to shock stage S3-S6 levels. The uniformity of shock features within all fragments shows that these fragments were not shocked in situ. Our shock data for mesosiderites, the absence of evidence of 3.6-3.9 Gy impact melt, the shock history of impact-heated ordinary chondrites, and the difficulty in quantitatively removing Ar in an impact event, all suggest that the mesosiderite parent body did not suffer a major impact event 3.6-3.9 Gy ago. Metallographic cooling rates of approximate to 0.03 degrees C/My at 400 degrees C were estimated from taenite lamellae in four mesosiderites using the latest diffusion coefficients and Fe-Ni-P phase diagram. Cooling rates of 0.01 degrees C/My at 425-325 degrees C were estimated from published compositional data for kamacite grains in four mesosiderites. These two techniques and four other semiquantitative, metallographic cooling rate indicators show that the mesosiderites cooled slower than any iron meteorite. We infer that cooling rates at 400 degrees C were similar to 0.02-0.03 degrees C/My and certainly less than 0.5 degrees C/My. The inferred cooling rate is too slow to allow Ar closure before 4 Gy. All of the shock, thermal, and age data for mesosiderites are consistent with slow cooling at depth <1 My after metal and silicate were mixed around 4.4 Gy ago. Thermal models indicate that the mesosiderites probably cooled in an asteroid some 200-400 km in radius. To elucidate the geological evolution of the mesosiderite stony-iron meteorites and their 3.3-3.8 Gy 40Ar-39Ar ages, we have investigated their shock and thermal histories. We have studied shock metamorphism in sixteen mesosiderites and find that none have been shocked to more than 10 GPa (shock stage S1-S2). Three mesosiderites contain a tiny fraction (approximate to 0.1% overall) of mineral fragments that were shocked to shock stage S3-S6 levels. The uniformity of shock features within all fragments shows that these fragments were not shocked in situ. Our shock data for mesosiderites, the absence of evidence of 3.6-3.9 Gy impact melt, the shock history of impact-heated ordinary chondrites, and the difficulty in quantitatively removing Ar in an impact event, all suggest that the mesosiderite parent body did not suffer a major impact event 3.6-3.9 Gy ago. Metallographic cooling rates of approximate to 0.03 degrees C/My at 400 degrees C were estimated from taenite lamellae in four mesosiderites using the latest diffusion coefficients and Fe-Ni-P phase diagram. Cooling rates of 0.01 degrees C/My at 425-325 degrees C were estimated from published compositional data for kamacite grains in four mesosiderites. These two techniques and four other semiquantitative, metallographic cooling rate indicators show that the mesosiderites cooled slower than any iron meteorite. We infer that cooling rates at 400 degrees C were similar to 0.02-0.03 degrees C/My and certainly less than 0.5 degrees C/My. The inferred cooling rate is too slow to allow Ar closure before 4 Gy. All of the shock, thermal, and age data for mesosiderites are consistent with slow cooling at depth <1 My after metal and silicate were mixed around 4.4 Gy ago. Thermal models indicate that the mesosiderites probably cooled in an asteroid some 200-400 km in radius.