Change template as link of visit

I use WordPress with two templates.

Of course first template runs when user visits the web page (it works correctly).

I would like that second template will automatically change when user comes from a set link. Do you know how to do it?

Both templates are almost the same (the difference is just second one haven’t header)

…

I was thinking maybe there are also the possibility to hide the headers instead of to change the template.

Thanks a lot.