It's a similar idea, but the code is structured a little differently, so here goes...
Start by modifying function qa_home_load_ifcategory(...) in qa-page-home.php:
1. Add $populartags to the global list at the start of the function.
2. Change the code below:
@list($questions1, $questions2, $questions3, $count, $categories, $categoryid, $custompage)=qa_db_select_with_pending($qa_db,
$questionselectspec1,
$questionselectspec2,
$questionselectspec3,
(isset($cachecountoption) && !isset($categoryslug)) ? qa_db_options_cache_selectspec($cachecountoption) : null,
qa_db_categories_selectspec(),
isset($categoryslug) ? qa_db_slug_to_category_id_selectspec($categoryslug) : null,
$pageselectspec
);
... to ...
@list($questions1, $questions2, $questions3, $count, $categories, $categoryid, $custompage, $populartags)=qa_db_select_with_pending($qa_db,
$questionselectspec1,
$questionselectspec2,
$questionselectspec3,
(isset($cachecountoption) && !isset($categoryslug)) ? qa_db_options_cache_selectspec($cachecountoption) : null,
qa_db_categories_selectspec(),
isset($categoryslug) ? qa_db_slug_to_category_id_selectspec($categoryslug) : null,
$pageselectspec,
qa_db_popular_tags_selectspec(0)
);
[All that changed is that $populartags was added to the end of the list(...) and qa_db_popular_tags_selectspec(0) was added at the end of the parameters to the qa_db_select_with_pending(...) call.]
3. Lower down in the same file, after qa_content_prepare(true, $categoryid); add the $populartags variable to $qa_content as follows:
$qa_content['populartags']=@$populartags;
4. Create a custom theme (see Advanced page on main site) and override the sidebar() function. Make sure your theme's sidebar() function calls the default one first via qa_html_theme_base::sidebar() otherwise your custom sidebar box will disappear. Then your function can do something with $this->content['populartags'], after checking isset($this->content['populartags']) since not every page will have it defined. To start with you can print_r($this->content['populartags']) to get an idea of what it contains. You can use qa_tag_html() to convert a tag to the standard HTML representation.