Pump question!!

A • mama to two beautiful boys 🤍

So I just got my haakaa today, I just put it on while nursing and got 2oz, now can I leave it in the fridge and pump into it again later? Or do I need to dump into a storage bag and start over? I'd like to save more than 2oz in a bag. I read somewhere you can't mix room temp and cold...someone please clear this up for me so I don't ruin anything!