Getting a little over 220 is no big deal at all, so no, I don't think you need an oil cooler if you don't drive hard and you're just seeing temps a bit above 220.
Keep in mind if you are regularly in the 250 - 270 range the engine won't go into limp mode but you are breaking your oil down a little faster and should probably at least consider a cooler or shortening your oil change intervals.
It's no big deal, really. 220 is about right.
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