How to display physical dimension fields on node--product.tpl.php?
Have you set the field to be displayed under display settings for the content type? 



Above is how the Field UI looks, maybe your product dimension field is hidden?

There is a guide here, on how to customize the Drupal commerce product display.

If you want to print the field in node--product.tpl.php you should first drag it so it is visible in the field UI.

Then you need to add render($content['product:field_width']);