If this is happening on idle. I doubt it has anything to do with PSU.
You need to replace the cooler. The i5 TDP is at 84w and the old i3 was running at 54w... That CPU cooler is not rated to be used on that processor. I wouldn't use your system until you replace it with a better cooler rated for your CPU.
https://ark.intel.com/products/80817/Intel-Core-i5-4460-Processor-6M-Cache-up-to-3_40-GHz
http://ark.intel.com/products/77490/Intel-Core-i3-4170-Processor-3M-Cache-3_70-GHz