It's routine for writers to input characters such as the degrees sign using ALT plus a numeric code (ALT-0176) for the degrees sign (°). Attempting to do so in Kate causes the cursor to show as "busy" and Windows then reports that Kate has stopped working. Other Word Processors on this computer do not experience this error, so it's a Kate problem.
I'm using the latest installer from https://kate-editor.org/get-it/ (17.08.1) and with this one I can not reproduce the problem. Can you try if you can reproduce with 17.08.1?
If you can provide the information requested in comment #1, please add it.
Have downloaded the latest build (took more than an hour despite an ADSL2+ connection getting 7.8MB/) and can verify that the problem is gone. Thanks :)
Great, glad to hear it!