Thanks to you both. That's really helpful.
I should add two qualifiers
1. The times Bellini cites for non-rotary is based on agitation every 30 seconds. So, rotary is a lot more agitation.
2. There is no cooling (well, there's a lot, but it's compensated for), because I'll be using my AGO, which has a tremendously accurate thermometer and adjusts time to falling temperatures. So, if I set it for (say) 6 minutes, it will never finish in just 6 minutes, as AGO will add time as temperature cools. But I do want to set the initial temperature as accurately as possible.
Color is not black and white, where it is possible to fully compensate for lower temperature by extending time. In color, this would lead to some issues with color balance. The old trick used much in the old days, was to use hotter chemistry, and experimenting that the required temperature was in the middle during the prescribed time for the volumes needed. AGO just adds time. The difference may be acceptable in shorter processes, such as C-41, but for E-6, the temperature difference is too great, as the solution will cool down quite a bit during 6 minutes. If you must use this system, I would recommend using a bit hotter solution than 38°C. Try with water and empty reels, what the temperature should be in order to get your AGO to run the first developing sequence in exactly 6 minutes. For other steps, this is not an issue, because they are all performed to completion.
Bellini kit is just their commercial E6 developers with starters added. So, these are totally standard chemicals, and the times given to the developer are exactly the same as for Fuji Hunt, or any other standard 6 bath E6 chemistry. And the time is officially 6:00, but with different opinions about the time making the best results. For instance, Kodak documentation suggested longer times for Fuji films, while Fuji Hunt does not. My personal opinion is adding a bit of time for Velvia 50, but not to Velvia 100 or Provia. In hand agitation, I normally use 6:30 for other films than Velvia 50, for which I use 7:00. For rotary agitation with a temperature control, I would suggest 6:15 and 6:45. These times are for fresh developer.