I've heard of similar problems, however I am baffled.
I have a Duron 900 (effectively), 256M RAM and do not ever have AI turns longer than 2 or 3 minutes. I have played huge random maps all the way through.
Have you tried emailing support at Infogrammes?
There has to be a reason for the slow downs that some people are seeing, but that others are not.
If you wish to email Infogrames go here:
http://www.ina-support.com/faq/civ3_pc.asp
scroll to the bottom and hit the *email support* button.
I would hope that they are collecting and comparing configuration information from people experiencing performance issues. Hopefully they and Firaxis can find a solution.