I am member of the Administrators group but I cannot open neither delete any of such folders.
That's because the explorer process does not run elevated. While your account is a member of the administrators group, you're still just a "user" until you elevate to get admin access. The default NTFS permissions on temp don't grant users read access.
Cleanmgr should be removing old files.
If you open a cmd or powershell prompt with "run as administrator" you can then delete the files.
In an admin Powershell prompt, you can play with this command to select how old a file has to be to be eligible for deletion. (Change the "10" to the desired number of days.)
Get-ChildItem -Path c:\windows\temp -File | Where-Object {($_.LastWriteTime -lt ((Get-Date).AddHours(-(24*10)))) }
You can then delete the files by piping them to remove-item. I would recommend that you do some analysis on file names and file age and think about what those files are from and if you should delete them or not.
Get-ChildItem -Path c:\windows\temp -File | Where-Object {($_.LastWriteTime -lt ((Get-Date).AddHours(-(24*10)))) } | remove-item -Verbose -whatif
Remove the -whatif switch to actually delete the files. Whatif is great for testing.
That won't remove empty folders, but it will delete files that occupy the disk space.
WARNING! Be very very careful when deleting files anywhere in c:\Windows. When Powershell first came out, I had to restore a VM twice because the application owner (who had admin access) was playing with Powershell and twice he deleted almost every file in system32.