Is there a cronjob I could use to delete a specific file every hour?

So, it would find a file called filename.txt and delete it.

What you need to do is write a PHP script to delete the file.
Then set it as a cron job by going to your cpanel and creating a cron job to call your script every hour.

I found something like this:

find /yourdir/tmp -mtime +1 -exec rm {} \; //where 1 is number of days since it was modified

However, I wonder if there is a way to change the +1 from days to hours. So, instead of deleting a file older than 1 day, it would delete it if it is older than 1 hour.

Does anyone know how to do that?

going off of you code, to do it for hours...
find /yourdir/tmp -mmin +60 -exec rm {} \\anything of one hour

try man find in your console or google it, you'll find def for -mmin option.