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.
Scripts are unable to run while your computer is powered off. What operating system are you running? How are you collecting the temperature? It is hard to give much more help without this information.
One thing I might suggest is powering on the system remotely at a scheduled time, using another networked machine.
Is there a way to leave python code running when the computer is shutdown?