The fire time of concern for a component within a used nuclear fuel transport package is the time after fire ignition when that component reaches its temperature of concern. In this work a legal weight truck package that is designed to transport one used pressurized water reactor fuel assembly is assumed to be in proximity to a 12-m-diameter jet propellant fuel pool fire. Container Analysis Fire Environment (CAFE) simulations are used to predict the fire times of concern for the fuel cladding, seal, lead gamma shield, and liquid neutron shield of the package, for different package locations relative to the fire under no-wind conditions. When the package was centered over the pool, the CAFE-predicted time of concern for the cladding to reach its possible burst rupture temperature (nominally 750°C) was between 11.8 and 13.3 h, depending on the modeling parameter values and mesh refinement. As the package was moved away from the pool center, the cladding time of concern increased, and its in-fire steady-state temperature (reached after being exposed to the fire for a long time) decreased. The cladding did not reach its temperature of concern when the package center was 6 m from the pool center (above the pool edge), even in infinitely long-lasting fires. This type of analysis can be used to determine a “safe distance” between the pool and package centers, beyond which certain components important to safety will not reach their temperature of concern, no matter how long a fire lasts. This will help risk analysts determine which accident scenarios can significantly affect public and environmental safety and those that cannot.