I just wanted to share an good article I followed yesterday when I needed to change the URL and therefor also the certificate in a Office 365 ADFS setup:
Remember always to use a public certificate in production environment and this is also required if you need SSO for you Office desktop deployment. You also required to use ADFS Proxy or publish ADFS though TMG if you need to use SSO.
I found this great video that explains how to publish ADFS though TMG:
!!!Remember as it also shows in the video, when creating the web listener and you are using a star(*) certificate like *.yourdomain.dk, that you type *.yourdomain.dk in the Internal site name.