Thickbox has a built in way to display content via AJAX. If you wanted to get your Url Action in there, you can do so like this.
<a href="@Url.Action("ActionMethod", "Controller")?height=200&width=300" title="My Ajax Content" class="thickbox">My link</a>
I looked through their source code and I'm not seeing any callback to easily insert the HTML response into the opened window.