So what do I do? Resort to web-based email access which our corporate server provides. This seems to work because Firefox seems to consume less memory, and is "more responsive" compared to Thunderbird. Also, the issue could be with thunderbird having to initialize a large email store (I have anywhere between 3000 to 4000 emails in inbox at any time). The headers are synchronized first, and are available instantly. But the loading the body takes a lot of time.
So here is the idea: Enhance thinderbird extension so that it helps open email using browser - assuming that your webmail can take the URL with appropriate ID, and allows you to login without losing that ID...
Small niceties always help.