If the bug was in thispage.aspx, you could simply fix it and apply the new page to the live site as a patch, knowing that it won't affect any other pages on the site. Since the bug is in the code-behind file, you can't do this without a full build and associated testing, etc.
Copy the code from thispage.aspx.cs to thispage.aspx (put the code in a <script language=CS runat=server></script> tag), and make these changes to thispage.aspx:
- Remove the namespace / class declaration
- Remove any declarations of controls as variables
- Change any "using" statements to <%@ Import ... %> statements
- Remove "Codebehind" and "Inherits" attributes from <%@ Page %> tag
Then for the next full release, fix the bug in thispage.aspx.cs and remove the above code from thispage.aspx.