Does turning on LED lights in a computer heat up your C inside? Is it better to turn it off? its only 1 blue LED about 10 inches long...does the led make the everything heat up faster or doesn't matter? does it generate HEAT?
Have you tried taking the case temp while it's been off for a while, and then turn it on for bit and seeing if there is any change?
Best way to find out is to test it out.
(The answer to your questions is that it's so close to being "no" it should be there, as in, in comparison to the amount of heat your computer itself is generating, the light is so miniscule that it wouldn't affect anything.)