Bob . . .
As for the routine you used for a 'very gradual' warmup, this from Bonita's experience posted on KoiVet this morning:
That Koi went from 37 degree pond water directly into 53 degree tap water and by the next morning the water had warmed to 68 degrees. In 14 hours she warmed by over 30 degrees. This Koi has been just fine staying outside over winter every year since that time.
FYI.