Oil in radiator

I have oil in my coolant . I noticed the oil was lower than it usually was so I added a couple of quarts then it started running hot but not to the point of overheating. when I looked in the reservoir I found where all my oil was going. help! this thing runs great and It dose not seem as if it has lost a head gasket. no water in the oil just oil in the water (strange) it will lose about 1 quart every 30 miles or so this sucks I am in the process of flushing and starting over what a mess . What are the chances of the oil cooler in the radiator leaking and is there a way to find out . Thanks Rob

.....no water in the oil just oil in the water (strange) ...
..strange indeed..though physically possible cause there are oil passages and coolant passages to the heads ..but quite unusual.
Oil cooler in radiator is transmission fluid...so make sure you identify the type of oil in the coolant....do you have whitish goo on the inside of engine oil fill cap?
.... if engine oil just "disappears", it has to go somewhere...oil pan, exhaust, asphalt...or....radiator ?!!!
You did not mention engine type...but I suspect a 3.1..
Are there other symptoms? poor/uneven heater performance, flickering engine temperature....the 3.1 is prone to head gasket failure....that would be no surprise..

This one has oil cooling lines on bolth sides of the raditor. I started taking apart the motor oil cooling lines from the raditor and water ran out so I would guess the oil resivor inside the raditor must be leaking inside. thank God it was not a head gasket. I think I will replace the raditor first then I will repost. Thanks Rob

My day is not lost: I've learned something: I checked at rockauto.com and they carry several versions of such. I guess this is a hot climate option that, for obvious reasons, we are not offered here in eastern Canada....or is it simply a towing option..??
..blown transmission coolers have been reported, so it figures that the same happens with oil coolers.
..it is a relief it turns out that way....

Well I took out the radiator today . I finaly got a day it was warm enough .
new raqdiator cam that I orderd online at cheap radiators .com $71.00
PROBLEM FIXED just need to flush out the system about 10 more times to get out all the motor oil out.