The more packages need to be upgraded, and the more repositories we have, the more space the update will occupy temporary.
To calculate this space from update to update is hard, but can be tested with the dry run solution described later if we have a test machine with the exact software content.
For a real time example, updating from RHEL 7.1 to 7.5 (desktop installation with Gnome) may take up 4 GB of cache space, but installation of a few fixes to a system that is only one or two months out of date will take up only a few MB.
To check how much space we have, we can use the notifies us in the above command's output on RHEL 7 versions, there may be orphaned data from removed or disabled repositories, which will most likely happen after minor release ugrades, in which case we can safely clear the data by hand: We may get more space for the update by clearing other data stored on the volume, like compressing/deleting old logfiles, moving large files to other volumes, or extending the volume size.
To work on with the possibilities of the next yum operation will work with the same directory structure, but on a different path - hopefully with more free space for the upgrade.
We can also move the cache to another volume by moving the whole directory: It is wise to know that the update will not fail on a trivial error such as low disk space.
Even with one or a few computers, we should gather information before starting an update of the whole operating system, just to be on the safe side.
One day there will be a problem, and it is much less stressing if you can solve it before it has impact on the actual job of a given machine.
To update the system you will need configured repositories that act as the source of the updated software.
If you sit next to the machine that is running the operating system to be updated, you can easily act if something goes wrong during update, like checking the output on the terminal, or boot to a live system if the upgraded one does not return from reboot - but this is not always the case.
To get this valuable information we can run the update process as it would run the actual update, but stop before any actual package downloading, installing or updating have taken place.