Maybe your overwriting the font-family of H3 later in your css file?
Edit: I'm quite sure since everything seems the work fine.
<div id="text-12" class="widget widget_text">
<div class="heading">
<h3>
Heading
</h3>
</div>
<div class="textwidget">Textwidget</div>
Note, I've changed the text to made it easier to read (for me)
I inspected your page. You may use some rule more specific to override the parent CSS file. For example,
#sidebar #text-12 .heading h3 {
font-family: "courier new" !important;
}