A 2x10 cylinder is pretty darned small, so I wouldn't see why the stock pump couldn't move enough oil. You might have foaming issues, which could cause your problems, more fluid would help if thats the issue.
You most likely do need more fluid capacity anyway, northern tool & equipment carries a bunch of small hydraulic reservoirs that would be perfect. Once you have added some oil capacity, cooling shouldn't be an issue. The use of an actual cooler shouldn't be required, as the volume of fluid in the tank will likely wick away enough heat. It's not like you are tying to drive a hydraulic motor, steering systems generally don't generate much heat to begin with.