With all the bickering that's going on in here, I want to ask something. Does it work? hot-cold, cold-hot, hot-hot, cold-cold? I mean, were you satisfied with the outcome.
Honestly, this isn't international politics here. We use a roux to thicken a liquid, period. Whether you need to strain it, heat it, cool it, doesn't matter. How you choose to do it for yourself doesn't matter. There is no right way versus wrong way of doing it, this is cooking not a physics proof. Sure there may be bigger, better, faster ways of achieving the same result, I'm happy for you, I'd love to learn your way of doing it so I have more options available to me. If you all want to go and bash on each other over the traditional french way of preparing a bechamel go ahead (and make a new thread please), but I think we're veering well off course of the original posters question and bordering on the edge of disrespectful here.
MICCRU: If your sauce is too thick add more liquid. If your sauce is too thin...well, don't let it do that, add liquid in batches, knowing proper ratios helps to.
p.s. get a scale, very important, use it constantly, it help maintain consistency throughout your cooking.
p.p.s. for those that care. I use cold milk, but that's my preference.