Each time I start kde the first time on a day, it opens a konsole window, and automatically dials in to my ISP using wvdial.

I much dislike this unwanted behaviour, which my system started some days ago, without any clear reason (no messing up with configuration or the like).

Kinternet is disabled by default, because I preferred manually editing /etc/wvdial.conf, and using wvdial directly.
The only automatism I created is a shortcut on the kde desktop to the "wvdial myisp" command, which is set to be run in a console window.

This all seems as if kde thought that it should run that shortcut whenever I log in. But why?

Could you give me an idea how to stop kde dialing in automatically?

Look for a 'ondemand=' setting in the configuration file for the connection and the interface (ppp0 or the like). If found set it to '0'. Normally a dial-on-demand is the culprit, as all it takes to trigger it is any service attempting to access the Internet.