The template for displaying all your posts should not be a custom page template. You should set the page you want to use as your Posts page in Settings > Reading. Then, as per the Template Hierarchy, your theme will automatically use home.php for this page, or index.php if that does not exist.
So you should save your template as home.php, without the /* Template Name: Blog Template */ comment, and set the page you want to use for displaying posts in Settings > Reading.