Thunderbird needs to download message headers, otherwise you wouldn't see anything. Whether you download an offline copy for all your messages is configurable. In Thunderbird it's called Synchronization. https://support.mozilla.org/kb/imap-synchronization

It did download the Headers, yes I know that, but thereafter it started download the messages 1 by 1 taking about 1 second per message

My Thunderbird inbox is also busy for 2 days downloading. .This is the culmination of several days trying to config T-Bird with Yahoo . This change was necessary because my ISP (Spiritone.com) was having real serious problems. Come to find out after a Frontier Tech spent 2 hours on my computer that Yahoo rejects T-Bird as insecure. By the time I got the message , the T-Bird config had gone through so many contortions that the continuous download had started and I can't stop it. Maybe it is all the hundreds, thousands?, of back emails that were stored while Spiritone.com was dark. Anyway, my thought is now to abandon the T-Bird account/app, dump it , and download a new T-bird app.

Carnal,

Unless you have something to contribute to KurtPloc's question, for your own problem please stick to your topic at https://support.mozilla.org/en-US/questions/1180816