I just finished my first complete cycle of yeast washing. I used the equipment shown in the video running around this forum (I already had all the jars & etc. from home canning so it was not much of a jump), and everything went just as shown.
I used the yeast cake (Wyeast 1056) from a double IPA that had been in the primary for exactly three weeks. I came out with three pint jars of yeast. At three weeks in the fridge, I pitched two of those jars on a barleywine, and had signs of fermentation within 4-5 hours. Yesterday, at 4 weeks, I pitched the remaining jar on an Amarillo Ale (this time just cold pitching), and had vigorous bubbling of the airlock overnight.
Conclusion: with this yeast, even with an extended primary, the washed yeast will produce a good fermentation, whether warmed or not, and no need for a starter.