Have a Nexus 5 (32 GB) and it's backlight is acting abnormally for few days!

I have this Nexus 5 for 11 months but for last 1 to 2 months it's backlight is like blinking and going off for several seconds and coming back again and partially dimming at a side and then recovering the brightness again. It started when I started playing clash of clans, and the phone got heated(around 45°C); but even after I uninstalled the game, it didn't stop. This is happening sometimes, everyday, but not all day long. That's why I wasn't concerned much, but yesterday after blinking for few seconds the bottom right side of the screen stayed a little dark(ish)[ not very prominent, but visible to me ]. It's still like that and still the blinking hasn't stopped. Anybody had this experience before, or anybody has a clue to fix this, help me.

P.S - The phone is fully functioning during this and, rebooting is ending the blackout, but that may be because the time taken for rebooting.