I'll put it to you this way. The hotter the oil gets (above 230) the engine makes less power. I found out the hard way back around 2003. We'd run a race and the drivers would start to complain after an hour that the engine was losing power. We'd start to notice that there would be a trail of black smoke under deceleration (i.e. going into turn one at Daytona). What I've found out is that the ECU is trying to save the engine by dumping more fuel in it and backing off on the ignition timing. The engine would lose power in about 40 minutes if we ran the stock radiator fan and shroud.
As long as the outside air temp was below 60 deg F, then the car seemed to be OK but then that all depended on the track. Places like Trois Rivieres were the worst as you never get enough straight line speed thus not enough air flow. When we would come in for a pit stop, it was not uncommon to see a small puddle of water under the car when it would leave. Some teams have tried bigger radiators and it would help but not as much as an oil cooler did.
The oil temp sensor does need to register the oil temp. If not, the ECU is confused and the engine will make less power. If you unhook the oil temp sensor, the engine uses about 30% more fuel and will even shoot flames out the tail pipe under deceleration followed by a big ol' backfire. It looks kewl but not something you really want to do.