Q: Would a faulty oil pump cause the engine to over heat? on 1997 Cadillac Seville SLS

Enthusiast 01be16a5a93688912f14755221fb15211b518d9a788cf01b455e03cc1bd585ac
Car has been over heating...replaced water pump and hoses, also did a flush. Everything was fine for a month or so, then had metal hoses ran fine again after a long distance trip. Now, car is back to over heating with the oil light blinking on and off...could it be oil pump? Also schedule to have head gasket replaced due to the over heating be on the safe side...err on the side of caution...
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The oil and coolant was not mixing...I broke down 8-( and had the head gasket replaced and things are much better now. Thanks for replying.