Thank you for your help to date, @Sass Drake, I really appreciate it!
Is there anything I need to do to bring this to the attention of the Avast team or will they see this post?
Just to summarise the current situation, I didn't like to shut down my computer with this unresolved for fear that something would be triggered when I rebooted, so I tried to remove all the suspect files to the "Chest". I have also tried to Delete them.
Running a quick scan immediately after, shows no viruses. But then when I run it again there are 70 or 80 files created again, always with the same name, MSIC5C7.tmp.
They don't appear in the Virus Chest and I can't see anything when I look in the C:\Windows\Installer location.
I have run Malwarebytes and Spybot Search and Destroy and they find no issues.
thank you