How to block Hot Network Questions in the sidebar of Stack Exchange network?

That's one of 50 or 60 enhancements to the SE user interface in the Stack Apps add-on SOX. You can load it from that link. You will also need a userscript manager installed for it to work -- Greasemonkey (for Firefox), Tampermonkey (for Chrome), or NinjaKit (for Safari).

To block Hot Network Questions, select the "Hide the Hot Network Questions module" option in the Appearance section of the features menu. The features menu will be accessible from a button added to the topbar:

BTW, another feature allows you to filter what is shown in the HNQ list by site and other attributes. The full list of features can be found here. Many of the enhancements are indispensible.

I would recommend installing the Development Version rather than the Official Version. The Development Version includes new enhancements but more important, it includes the latest bug fixes (and rarely introduces new bugs). SOX is used on a wide variety of platforms, browsers, and configurations, so that's an easy way to avoid a potential problem someone else discovered and has already been fixed.

I wrote a Chrome extension to hide/filter the Hot Network Questions list last year. As well as hiding it allows you to filter the links with a site or keyword whitelist or blacklist, because I found that though certain sites were usually distracting, others were often useful.

You can install it from the Chrome Web Store or check out the code on GitHub. (Originally shared on MSE).

Using uBlock Origin on Windows 7 with FireFox 50.1.0 I was able to achieve your desired result with this:

FWIW: I prefer uBlock Origin 10-fold over ABP.

ABP is a sell-out but they do allow you to disable their acceptable ads.

uBlock feels faster and it is WAY easier to just temporarily unblock a site and re-block it.