How to retrieve email at old host?

I transferred a domain (www.mydomain.com) from one hosting provider (OLD-CO) to a new host (NEW-CO). How can I download email that is still sitting at OLD-CO, to my desktop?

Some email accounts have 10,000 or more emails, so using the Web email client is not an option. I still have an account at OLD-CO, and I have access to the DNS records at OLD-CO.

AFAIK my desktop email client requires that I specify the POP address (pop.mydomain.com). This points to NEW-CO, not OLD-CO. Are there any desktop email clients that can use an IP address instead of a domain name?

I could change the MX record at OLD-CO. How would I configure the desktop client to access it?

I prefer using an email client that stores email as plain text, like Eudora. I have written code to extract email addresses and other information from the desktop copy of the emails.

Chances are you can access the OLD-CO's mail-servers directly. It won't be 'pop.mydomain.com', but 'pop.most-other-domains-at-old-co.com' will probably point to the same actual servers serving mail. Your login should be the same and is probably [email protected]. That should still work even if your domain is being hosted elsewhere.