randomSEHotLink.user.js

// ==UserScript==
// @name         Load random Stack Exchange network hot question
// @namespace    http://edcottrell.com/
// @version      0.1
// @description  try to take over the world!
// @author       Ed Cottrell
// @include       *://stackexchange.com*
// @grant        none
// ==/UserScript==

var hotLinkCount,
    randomHotLink,
    randomHotLinkNumber;

if (location.search.match(/[?&]\brandom\b/)) {
    hotLinkCount = $('a.question-link').length;
    randomHotLinkNumber = Math.floor(Math.random() * hotLinkCount);
    randomHotLink = $('a.question-link:eq(' + randomHotLinkNumber + ')');
    document.location = randomHotLink.prop('href');
}