Chemical kinetic thermal decomposition models of pressed solid high explosives containing octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and triaminotrinitrobenzene (TATB), which accurately calculate the times to explosion at various initial temperatures measured in the one-dimensional time to explosion (ODTX) test, are extended to higher temperatures to predict the critical temperatures, times to explosion, and dimensions of the impact- and shock-induced hot spots that are known to control the ignition of exothermic reaction in solid explosives. The effects of hot spot geometry and surrounding temperature on the critical hot spot conditions are investigated. Since hot spot temperatures and dimensions cannot be measured experimentally, these estimated temperatures, sizes, and times required for exothermic chemical reaction provide a means to evaluate proposed physical mechanisms of hot spot formation in accident scenarios involving impact (friction and shear) and shock compression of solid explosives.