I'm with Irish.
But to directly test your concern, get a thermometer (grab the wife's turkey thermometer, hehe) and put it in the box, go check it at the highest heat of the day.
Kerosene has a flash point 100–162 °F and an autoignition of 428 °F. If you can keep the Kerosene below 100°F, then you don't have a problem. You could store it at higher temperature if you could be 100% certain no source of spark will be present. If it were to reach 428 °F, no spark would be needed as Kerosene will spontaneously combust at that temperature.