Computer exceeding maximum recommended temperature?

I recently bought a new custom made computer. It's processor is an Intel i5 and it has 8GB of RAM and its graphics card is Intel HD Graphics 4600. It isn't special for gaming or anything but it is quite powerful and cost me around $1100. I don't play any games on it except for Minecraft. Whenever I play Minecraft, after about 30 to 60 minutes, an error message pops up saying:

[Processor Core 3 Temp.] exceeded its recommended maximum temperature.(90 degrees)

(The last degrees part usually varies between 70 and 90 degrees.) Sometimes this message pops up after 10 minutes of playing the game. Whenever this message comes up, I usually turn the computer off and allow some time for it to cool down. This really annoys me because I want to play Minecraft but I can't.
Why does this message come up? And is there anyway to stop it from coming up or maybe allow me to play for a little longer before the message come up? I have Minecraft set to the lowest settings possible but that doesn't make a difference. Also what happens if I keep on playing after the error message comes up? Will it melt my computer because its too hot?

It sounds like either your CPU (I5) heatsink is clogged with dirt or the heatsink on your CPU needs an uprgade.
most likely just clogged with dirt.

Because your pc is heating up more than you think. You can try a new cpu coolor. It will solve the current cooling problem. No need any other change. I'd prefer Cooler Master Hyper 212 Evo air cooler. It quite suits for gaming and a heat beaker. No worries. Cheerzz

Maybe it could be your cooler. Try a new cooler
Or it could be less thermal paste or more thermal paste which is causing the problem.