It looks to me it is more of a "Lastest active threads" than a "hot" topic.

Shouldn't a thread needs certain amount of posts before it becomes "hot"?

I feel that the front page provides a good way to view new topics that would otherwise get lost.

Agree - its just a wording thing. I think it should be called "Recent active threads" or something like that.

On the topic - "Recent Forum Activity" on the sidebar I think needs a slightly different name. Something like "My Recent  Activity"

I absolutely agree. I check only threads with my posts (Recent Forum Activity) and hot topics. Sometimes there is big explosion of sucker topics which force really hot stuff out.

ioi,
Well, it is a little confusing. It literally took me weeks to understand that the sidebar actually shows the threads of my latest posts. Before that I would use the sidebar but always wondered how it worked.

 That would result in some threads with huge amount of posts, and a lot of threads with no post, because a lot of people using the "Hot topics" rather than browsing the forum. 

I personaly would take it completly of the page, but i think many would disagree.