I can't believe jamz4 said that. I am ashamed that I almost laughed.
LCD/LED do not emit harmful rays. Older CRT monitors and older CRT based Televisions (the big bulky boxes) do emit harmful rays and will damage your eyes.
Getting too hot in front of the monitor/TV is most likely a biological effect of getting swept up in gaming, and your adrenaline starts to pump. It makes your heart beat faster and your body temperature can rise. I recommend using a ceiling fan or air conditioner to keep temperatures pleasant.
Also, if you're sitting too close to your computer box, it may be putting out some heat as well.
Now, as far as eye damage with modern LCD/LED displays... there is a threat from "glare" and "brightness" but not from harmful radiation. A nice, simple pair of glasses that have an anti-glare coating on them will reduce the glare and reduce eye strain during long periods of gaming. Since I bought a pair of anti-glare coated glasses for my computer use, I have been able to double the time I can sit comfortably in front of the computer without eye strain. Should be required for people who have to work in front of a computer screen for 10+ hours per day.
OH CRT is very harmful actually I spend at least 14 to 15 hrs a day... Playing games, browsing web and doing some productivity works. Thanks