Agree with Yooper and do my lagers similarly. I initially chill the starter below room temp so I'll get better aeration. Ferment the starter(s) at room temp and such that I'll have a good 24-48 hours for the last starter (if there were steps) to chill/settle in the fridge. Chill the beer below fermentation temp, aerate extremely well, and then decant/pitch the yeast straight out of the fridge. No need to let it warm up, it should take off very fast.
I even pitch ale starters straight out of the fridge and they take off very quickly. Look up 'cold-pitching' for more info on that. It works.