I don't really think this is worth the coding...it's not that hard to just check the page, if it is a really popular thread, then it will be near the top.
Even better, there could be some sort of code that takes into consideration how often replies are left, how many replies are there, etc. So it would be a more accurate way to determine what is currently the most popular thread.
As to putting it on the front forum page, I am not such a fan. I like the idea of keeping it clean and uncluttered. I think that if something like this was implemented, it would need to be something that was perhaps brought to the top in the actual forum section.
Well, if it always shows the most popular topics, people would always reply there and it would remain the most popular. I don't like this idea because it really isn't needed. What use would it have? I agree about what Ricador said, if it's that popular it would be near the top of the list.
Disadvantage: What if the topic has the most replies but you don't like it or not that important. (Although you can see others)
I think it's just more of a 'if your looking for a hot-spot' on that forum type of thing, if you don't like it then you don't have to click that and just simply do things the old fashion way =)
But I like it, I mean it will defiantly give you some insight to what's popular in the forum right now, plus it saves you the time of looking for some forums you want to get into and talk in a good discussion about.