Backlight Problem

Hi, I've been having a recurring problem with my laptop. If the laptop falls slightly falls slightly below room temperature, the backlight will not light.  Over several minutes, it'll heat enough to lighten--I won't have a problem until I turn off the laptop and let it cool. A blow dryer or body heat hastens the process.  I'm wondering if this is a normal occurence;  I doubt it is.  If I were to have Dell replace the backlight, would anyone know how much it would cost?  Thanks.