80+ Mail console messages per seconds: "no entry for mailbox id  in the cache; this should never happen" Mail rarely below 30% cpu on a 2.8 GHz Quad-Core Intel Core i7 …
-> could be 100% of one core …


fan on (very loud), top of the notebook very hot,
laptop very slow to react/respond to inputs
making Mail unusable / stopping it makes the machine quieter/colder/reactive again
Weird part is: trying to troubleshoot, when toggling off all mail accounts (and even tried notes), the Mail program is still sending the message:
"no entry for mailbox id [variable ids] in the cache this should never happen" to the console - until some timeout seen once - making me think the issue was solved, but it came back.
all the same Mail/Notes accounts seem to be ok on iOS though …
no related topics found on google, except problem with accountsd maybe …
seems to be a feature post install Catalina ...
although similar messages appeared in this thread in 2009:
https://discussions.apple.com/thread/1891181
suggestions/comments/same experience anyone :) ?
Same problem for me and this have solved :

Quit Apple Mail

Go to folder : ~/Library/Mail/V7/MailData (you should use the Finder &quot;Go&quot; menu then &quot;Go to folder&quot; because this folder is normally hidden.
~ is your user home folder.

Rename all &quot;Envelope Index xxx&quot; on &quot;--Envelope Index xxx&quot;. You should normally have 3 (on the screenshot I have 5 files but it's because Apple Mail was launched when I take it).

Launch Apple Mail


Normally, Apple Mail will re-create this files that are cached data and all could be solved.
Jérôme.