Custom template for CPT

Hi Tom!

I have created a CPT and I need it to use a custom template for displaying content.
I've used custom templates before but I can't figure out how to assign it automatically to the appropriate CPT.

Also, I think I should customize single.php and content-single.php as both are involved in displaying single post content isn't it?

So, is it some function I can use in order to make CPT "mycpt" use "mytemplate" instead of choosing it manually everytime I add another entry?

Thanks in advance!