Yeah, I wouldn't worry too much about the temp of the sparge water. The main this is not to let the grain bed temp get above the 170-175*F threshold. My understanding about tannin extraction is that it is a combination of the temp and the pH climbing through the sparge process. Otherwise, batch spargers would have have tons of tannin problems and they don't.
I usually sparge with water in the 175-180*F range after mashing out and the grain bed temp will actually fall or hold at 168*F for the duration of the sparge.
Drinking on the keg: BPA, Brown Ale, Dry Mead, Wee Heavy aged on Oak, CAP
Drinking in the Bottle: