I personally would not recommend keeping the light on all the time, corns are naturally nocturnal and are most active at night and leaving the light on may cause there natural activities to become messed up affecting their immune system, growth rate etc. In fact my two only ever come out after the light goes out. I also read that some people think it may even be a good idea to adjust the time the light is on to mach the seasons i.e. shorter in winter than in summer as it would be in the wild.
Anyway about a month or so ago my timer for the light stopped working so I left the light on all the time for about two weeks till I could get to the shop that sells them, and my two corns both stopped feeding and the female got in a VERY bad mood after a couple of days, trying to bite me and all sorts and she would not normally even think of.
As for it getting a bit cold of a night, I live on the east cost and the wind makes nights very cold (my viv is 6ft x 3ft x 4ft with only one heat mat that covers about 2 1/2 - 3ft of the hot end) and my two don't seem to be bothered by it much at all and will often choose to use one of the hides in the colder end of the viv even when the temp is quite low. However if you think that the temp is getting to low for them a couple of options are, either to get another heat mat and put it on the back of the viv in the hotter end or, I read somewhere that red lights will not affect their normal nighttimes activities, although I have not tried this. Either way you can have timers switch on stuff as it switches other stuff off so you don't have to mess about doing it your self.
I am sure this sounds strange but my corns seem to be happier when I treat them as I would like to be treated, decent varied food, comfy surroundings, stuff to interest me etc. and I do not know about you but if someone made me have a bright light on 24/7 I would soon get pretty pissed to say the least