How to theme a blocktitle of a view?
Have a look on the original template on modules/block:

&lt;div id="&lt;?php print $block_html_id; ?&gt;" class="&lt;?php print $classes; ?&gt;"&lt;?php print $attributes; ?&gt;&gt;

  &lt;?php print render($title_prefix); ?&gt;
&lt;?php if ($block-&gt;subject): ?&gt;
  &lt;h2&lt;?php print $title_attributes; ?&gt;&gt;&lt;?php print $block-&gt;subject ?&gt;&lt;/h2&gt;
&lt;?php endif;?&gt;
  &lt;?php print render($title_suffix); ?&gt;

  &lt;div class="content"&lt;?php print $content_attributes; ?&gt;&gt;
    &lt;?php print $content ?&gt;
  &lt;/div&gt;
&lt;/div&gt;


As you might see in line 4 there is a 

&lt;?php if ($block-&gt;subject): ?&gt;    
&lt;h2&lt;?php print $title_attributes; ?&gt;&gt;&lt;?php print $block-&gt;subject ?&gt;&lt;/h2&gt;
&lt;?php if ($block-&gt;subject): ?&gt;


Use this... but do not forget to use 

&lt;?php print render($title_prefix); ?&gt;


before the title and 

&lt;?php if ($block-&gt;subject): ?&gt;


after the title - these variables enable contextual links.

Additionally assure that you follow the template naming conventions. I think it should be views--view--my-view--block-1.tpl.php (but I am not sure - did you alreay find out if your template file is used? To do this just add any text into the file to see changes in the browser).

When you just added a new template file remember to rebuild theme registry. Either by deleting all Drupal caches or by visiting admin/appearance. If you use Devel module in conjunction with Admin menu you find a possibility to rebuild the theme registry under the projects favicon on the left of the Admin menu.