Quick Update:
After unnistalling Adobe Creative Cloud and all its applications as suggested, killing all processes and re-installing - the problem persited.
I got tired of fighting the issue, so I went on a break and let the computer alone for a couple of hours while the fans ran at their full and the CPU was 100%. When I came back CPU was normal, no more crazy fans.
Not sure if whatever process the CCXProcess was running finished and it was just something that took a lot of CPU and a loooong time to complete.
I am just glad my computer is back to normal.
Daniel, and others, I am sorry that you continue to see high CPU usage. This public discussion thread is currently full of both individuals and people who work for organizations that manage their membership and computers.
If the computer and membership you are using are managed by an organization, please contact your organization's Creative Cloud plan administrator. They can use the process listed https://helpx.adobe.com/enterprise/using/support-for-enterprise.html to contact us on your behalf if needed.
If you have an individual membership and have full control of the computer and network, then please download and run the CC Log Collector Tool from http://helpx.adobe.com/creative-cloud/kb/cc-log-collector.html and begin a secure chat session at https://helpx.adobe.com/contact.html?rghtup=autoOpen. Our support team will work with you directly to analyze the logs and determine the cause of the high CPU usage.
Thank you, everyone, for your continued patience. Please take advantage of the support option that is appropriate for you to contact us directly.
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