Ret.Bugtech is probably right . . . he usually is . . . at least 99.99% of the time. The other .01% of the time he's probably at least half right too.

There may be some "good" chrome engine tin out there, but most of it I've seen looks fantastic, but comes up really short in the "fitting correctly" and "directing the air to where it needs to go" catagories. The original black tin absorbs heat from the engine and radiates it outward much better than chrome, which tends to reflect the heat back to the engine. I remember seeing some test results somewhere many years ago that showed the difference in temperature due to chrome vs. black tin. It wasn't drastic, but like Ret.Bugtech said, chrome does make it run hotter. That's a documented fact. Still, if everything else is OK and it's basically a stock engine, it shouldn't be enough to worry a lot about.
But, if you add on top of that a slightly incorrect timing setting, a few air leaks in the cooling system where the tin doesn't fit correctly, part or all of the engine bay seal missing, etc., etc. all the little things add up . . . then throw in a couple of days with temps near triple digits . . . you can have a major melt down in a hurry.
I'd start with the timing and make sure it's set correctly, and make sure the engine bay seal in intact. Those two are a MUST, then start looking for other issues. I love the look of chrome, but if it came down to LOOKING cool, or actually RUNNING cool, I'd ditch the chrome if necessary. But if you get everything else right, you should be able to get away with the chrome.