I have a python script that checks the temperature every 24 hours, is there a way to leave it running if I shut the computer down/log off.
Shutdown - no.
Logoff - potentially, yes.
If you want to the script to automatically start when you turn the computer back on, then you can add the script to your startup folder (Windows) or schedule the script (Windows tasks, cron job, systemd timer).
If you really want a temperature tracker that is permanently available, you can use a low-power solution like the Raspberry Pi rather than leaving your pc on.
Is there a way to leave python code running when the computer is shutdown?