I have always said that when drilling, the attention should be to make a good chip - the hole is the by-product.
Using "coolant" is almost unneccessary. If the chip is formed properly and the speed and feed are good, the chip will take most of the heat with it. Coolant will help keep the heat from building in your part or in the tooling on long tool cycles. Cutting fluid helps reduce friction, but not where the cutting is occuring - it helps lubricate the chip in the flutes and provides a barrier to keep the hot chip from transfering heat to the flute. - think about it - how is any cutting fluid going to reach under the chip to actually get to the cutting edge? It doesn't. It lubricates the land areas and face of the flutes and the keeps the chip moving along.
I rarely use either coolant or oil for drilling steel. I will use fluid for drilling aluminum to keep the AL from galling in the flutes. I always use a sharp drill. The drill should not be hot after drilling a hole most of the time - if it has adequate clearance and is sharp, it will be slightly warm from chip friction, but it should not be hot. If so it is either dull, has inadequate clearance, you are spinning it too fast or you are feeding too aggressively. There are a lot of situations that will cause a drill to get hot - I know - but generally speaking it should remain handleable after drilling - without coolant.
Go as slow as you can to make a curly, silver chip. If the chip is blue or black, back off on the pressure. If it is not curly or stringy, back off on the RPM or increase pressure. If the drill is squealing, back WAY off the RPM, sharpen the drill properly or get someone else to make the hole for you.
Make the chip and the hole will be there.
Scott