The cooler sounds like a good temperature; your must can get quite a bit warner than ambient temperature anyway. I've got mead at 15 degrees Celsius ambient and its still fermenting happily.
I believe that you were meant to soak the oak to soften the flavour. Wine makers don't age in brand new barrels, they put them through a bit of use first. So if anything I think you'll find the wine is too woody! Alternatively they might just be saying to do that to sanitize the wood?
I'd give it a taste, and if its getting a bit much I'd consider racking off the wood. Not certain of this though.
"If the beer you are drinking is dull, perhaps its makers are telling you something" - The World Atlas of Beer