Each site got a "hot" tab, where its contents are calculated based on this seven years old formula.
However take a look on the screenshots below and see for yourself that "hot" got nothing to do with many of the questions listed there.
As you can see, there are questions with negative score, no answers, and even closed. I won't be surprised to see spam in there as well. This can't be any worse.
What I suggest, instead of fixing the formula or patching it, simply have the hot tab show the same questions as the Hot Network Questions sidebar. (from the specific site only, of course.)
Since the hot questions "pool" (as seen here) is limited to 100 for the whole network, either expand it or have the per-site list show questions with less hotness points - it would still be better than what we have now.