Short answer ... the only way to be certain that the print spool releases all pending jobs is to turn it off first, then delete the .tmp files. That said, if you don't stop it, you can safely delete the files first. Reboot ... should they return, you'll need to stop first then delete.
I just looked at my system32 folder, there were about 30 .tmp files from 2016 (likely when I replaced my printer). I did not stop the spooler, just deleted the files. They are gone gone.
You might check to see if you have the most current printer driver installed. A simple way to do that is to run the Windows 10 Printer Troubleshooter:
Right-click your Windows Start menu
Click Settings, then Update & Security > Troubleshoot
In the Troubleshoot section, under Get up and running, click Printer
Click Run the troubleshooter to begin
Alternatively,
Settings > Devices > Printers and Scanners, click the printer, click “Manage,” and click “Run Troubleshooter.”