Do you have synchronization enabled for your IMAP account? https://support.mozilla.org/en-US/kb/imap-synchronization#w_disk-space-usage

You should have seen a setting to store messages on this computer. Clearing this should stop the further download of messages bodies. I'd remove the account in Thunderbird, add it again, with this setting cleared, then find and remove the old data files to free up disk space. Do you have no other disk drive you could move your storage onto?

I am assuming this is an IMAP-connected account. Don't delete the messages in Thunderbird as this will also delete the synchronised folders on the server.

I believe that if you cleared this setting, then closed Thunderbird, opened the profile in your file manager and removed the relevant files under ImapMail this would have the required effect; you'd remove the downloaded messages without forcing synchronization. But I'd need to set up a temporary account to check this without the risk of losing stored messages, if it doesn't work as I hope for.

Yes, I just tried this with an expendable account and it seems all OK. The messages remain on the server but there's only a few kb taken on the local HDD.

Thanks for your suggestions. Unfortunately it seems that Thunderbird does not the clean up work by itself. You have to change the settings AND delete the files.

I found in the internet the hint to close Thunderbird and then delete all files in subfolders of folder "ImapMail" execept for "msgFilterRules.dat". After restarting it fetches the files according to its settings.

Well, yes, I did say so:

…if you cleared this setting, then closed Thunderbird, opened the profile in your file manager and removed the relevant files under ImapMail…

When you remove an account from Thunderbird it doesn't delete the account data. This is a useful insurance policy against accidents. Users often remove an account and then express surprise that all their messages have vanished. It's not clear why they think it should do anything different.