Unfortunately, it can't. Nuclear reactor cores can obviously get very hot, but for safety reasons they are not allowed to. They work at about 300 degrees Celsiu

Unfortunately, it can't. Nuclear reactor cores can obviously get very hot, but for safety reasons they are not allowed to. They work at about 300 degrees Celsius. The linked heat engine has the high efficiency quoted only when the hot element is extremely hot, a few thousand degrees Celsius.