I share your concern but proposed solution seems a bit too hard because it would cut network wide "advertising" of a new site right at the moment when it can seriously benefit of being promoted at sidebar.

I would prefer a softer approach by limiting amount of hot questions from such sites by 2 or 3 instead of default 5.

On a more general note, the very default of 5 questions limit seems to be worth reconsidering.

While checking hot questions list I noticed that besides PLDI, some other sites also have many questions there. When I additionally checked that, it turned out that not just PLDI - 9 (nine!) more sites have 5 questions in the list.

As a result, 10 sites occupy half of hot list, leaving mere 50 slots for about 200 other sites in the network. This feels so very wrong.

I think it would be better to decrease default limit from 5 to 3. Maybe this would also allow us to keep system simpler by avoiding customized limit for new beta sites.

Another worrying thing I saw is unjustified advantage given to questions with multiple answers.

4 out of 5 PLDI questions I saw in the hot list had 4 or more answers - and three of these four questions were stuck there for more than a day. That made me curious about other "over-represented" sites and when I checked, it turned out that most questions from these ten top-hot sites had 4 or more answers (30 of 50, to be precise).

This may relate to concern raised by PLDI moderator in comments here:

I don’t even think it’s a particularly good sample of our questions. Of course, that’s a general problem with HNQ—it tends to elevate clickbaity questions, which are rarely the best quality

I don't participate in PLDI but based on observations on the sites I am better familiar with, it indeed looks like current preference to multiple answers tends to give skewed presentation of site topics and posts quality.

I think if cut off value for hotness score calculation was decreased from current 10 answers to 3 or 4, this would lead to better balanced and more diverse representation of the network questions in the hot list.

Isn't this the whole point of private beta?

We did have a few weeks to find our feet before being advertised in the HNQs: that's the whole point of private beta. And there was only a week or two in between us going public (=being in the HNQs), and us getting mods (that delay being the time the election took).

If community moderators are the issue, I would suggest as a feature-request to not start the public beta stage until pro tempore mods are elected. But restricting public betas' access to the HNQs? No way. We earned that.