No. I've been running over 400bhp for 3 years now on K04's. On a few occasions when pushing it hard i've had elevated oil temps which pushed the coolant over 100 degrees as a result, but I didn't have a seperate oil cooler fitted. That was also only happening when ambient temps were pretty high (eg: 18+).
I've now fitted an oil cooler and know that the stock radiator will do a more than satisfactory job of keeping the coolant at the right temps when it's not got to cool the majority of the oil as well.
Another point to consider is that the stock radiator has the gearbox oil running through it to provide some cooling too. Unless you planned to fit a separate gearbox oil cooler, you would need to make sure the custom rad had this as well.
And as mentioned previously, 2nd hand rads can be picked up fairly cheaply. I cracked my 3 year old rad when pulling the lower hose off recently and managed to pick up a decent condition 2nd hand one for about £50 delivered. Job done.