I'm sure there are people who believe passionately one way or the other, but I don't think it makes any difference as long as you whisk like crazy as you add the liquid. And I agree with @oldunc that a flat whisk works perfectly for this.
Left to myself I add it hot, all at once (this is where you need a flat whisk), but I've followed recipes to do it every which way, and had no real trouble with any of them. Just make sure to whisk while adding the stock (or milk or whatever)- dumplings can form pretty fast.
My answer is as a home cook. In my experience I have used room-temperature stock and even stock that I had in the fridge. I added it directly to the roux and had no trouble. I find that my gravy/sauce is smoother if I slowly add the liquid while constantly whisking. When I have dumped in all the liquid at once it has resulted in lumpy gravy. But, even that is fixable if you strain through a fine mesh strainer... :)
"Classic technique" states that one should always add cool liquids to a hot roux and vice versa, but I have never found that to be necessary. Since I'm going to heat the liquid to fully activate the thickening power, I would add a gently simmering liquid, slowly, to the roux. If its a small amount, I'll stream it in as I'm whisking vigorously (important at the beginning of the liquid's introduction)...if its an unmanageable amount, I'll ladle it in.
"Classic technique" states that one should always add cool liquids to a hot roux and vice versa, but I have never found that to be necessary. Since I'm going to heat the liquid to fully activate the thickening power, I would add a gently simmering liquid, slowly, to the roux. If its a small amount, I'll stream it in as I'm whisking vigorously (important at the beginning of the liquid's introduction)...if its an unmanageable amount, I'll ladle it in.
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