In Settings/Reading I set Testimonials as post page.
How can I change the header of that page?
You could use a template. You just have to copy the file
then you can call your custom header with
See the template hierarchy. Just be sure Testimonials is your front page.
EDIT: Regarding front page (1rst page of the site) WP looks into your theme and the first file to be called is
Here your can set another file as custom header and call it in
You could also insert some conditional tags in the main