While you didn't reveal details, the 60C is a known set point for throttling so it is indeed heat related. Your newer techs will write it's not heat but you proved there is a heat issue in your post.
Also, you are measuring just a few chips and what if there was a motherboard or other chip that didn't like the elevated temps?
As to the PSU, the make, model and the rest of the machine is not revealed. Here's my rule for PSUs. 1. Have 50 to 100% spare AMPERES. Not Watts! 2. Most folk can't balance the +12V rails. Make sure you have a single rail +12V PSU.
Finally, if fans are like you noted, fix that.
Recently, my computer has started freaking out when I play games that are even semi-demanding(League of Legends on mid-high settings, KOTOR 2). The fan starts running on max and it sounds like it is hitting something, like maybe a piece of dust/plastic is stuck in there. I haven't opened the case yet to see which fan it is. Then, usually after about 30-45 minutes(and getting worse) it just crashes. No error screen, nothing. Just reboots as if I just turned it on. I have downloaded a couple different programs(CoreTemp and OpenHardwareMonitor) to check if something was overheating and nothing is. It tops out at about 60 C when in use. The only things I can think that I've done recently is switched my monitor out for a Samsung Smart TV and upgraded to Windows 10 about a month and a half and two months ago, respectively. I've considered that maybe the PSU is crapping out, especially since I've always had weird issues with USB/other ports not working properly. I want to cover all of my bases before I go off spending money on a better supply though. Any tips for fixing this would be much appreciated.

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