The probable cause of the undercowl engine fire was the burn-through of the combustion chamber inner liner from the accumulation of dust that became molten during operating and infiltrated the combustion chamber thermal barrier coating causing it to spall off and accelerate normal thermal distress. The burn-though of the combustion chamber caused downstream hardware to experience higher than designed temperatures that resulted in mechanical and thermal distress to the point that the low pressure turbine case began to melt. Contributing to the combustion chamber failure was the operators' failure to do recommended borescope inspections that would have detected the combustion chamber distress and hence the removal of the engine before it was allowed to progress to the point that the combustion and turbine sections of the engine failed.