How to fix Civ 5 graphics

I bought Civ 5 on the Steam sale recently, but it's really hard to play as I'm getting these really bright coloured patches appearing and disappearing on the screen after a bit of playing. Then the menu becomes a mess of random colours after exiting a game. This happened with the graphics set to max and when they were set to the minimum and I have a pretty good computer.

I'm running it on the DirectX10 & 11 mode as recommended and I can run Saints Row 3 in the same mode with no problems. How can I fix this?!

Edit: added some pictures I managed to get

I had almost the exact same problem, and fixed it with the "verify cache" option in steam. That may solve your issue too.

Graphical glitches usually occur because of some hardware issue. Graphics cards get especially hot when working through loads of data, so proper cooling is a must. Therefore what you're experiencing sounds more like a hardware problem than an issue with the game itself. Have you tried running the game on lower resolutions, turning down the fanciness to see if the same thing happens?