Increase Text Box Size

If the Heading Here layer is a nested composition, you will have to edit the composition settings to make it bigger. That will cascade into a lot of other changes.

If the template is efficiently designed, the size of the header text will automatically be modified, so everything always fits in the layout. Without seeing a screenshot of the flowchart to show the comp and nested comp structure for the template and also a screenshot of the timeline with all of the modified properties of that layer revealed, the only way I can have any idea how they set up the project would be to download it and fiddle around. 

If you can't figure it out by watching the tutorial like Mylenium suggested, embed some screenshots. Please don't link to them. Just drag them to the reply field, copy and paste them, or use the toolbar. Maybe we can figure out a solution if we can see how the project is set up.

Well, have you actually downloaded the tutorail that comes with it? It may already explain everything. Otherwise I would bet there's some sourceRectAtTime() expression at work on the black box and it may simply need to be modified, but without a screenshot of the actual expression in the timelien and all that nobody can tell you much. Templates tend to be set up in a very specific manner for their customization mechanics to work...

Mylenium