Page rendered correctly but display errors
First of all, the 'und' is not prefered, you should use LANGUAGE_NONE constant instead. This is not part of the sollution, but part of the Drupal coding standards.

This is a tricky one. The function render() expects a string, but you give a part of an object with some deeper array keys.
The simplest way to get around the strict warning is to use the following code:

&lt;?php $uri = file_create_url($node-&gt;field_header_image[LANGUAGE_NONE][0]['uri']); ?&gt;
&lt;div id="hero-container" class="hero-container" style="background:linear-gradient(rgba(0, 0, 0, 0.35), rgba(0, 0, 0, 0.35)), url('&lt;?php print render($uri); ?&gt;');"&gt;