That is what I did initially.
But Aussibear's solution was even better. Now, everything is done when opening the workbook (new sheet with current date if it doesn't exist, model added to that new sheet). It is just more efficient.
What I initially did worked fine, Right click on a sheet -> Insert and insert the xltx file. I just had to fill the table with data in that sheet and save.
Maybe that is not really the correct way of doing it, I don't know.
Now it is just an hidden sheet in the current workbook.