Opamps can drift and the data sheets usually show how much they will drift.
It is not normally a problem at room temperatures, though, unless you try to use very high gain.
If you are amplifying AC down to 40 Hz you might be using electrolytic capacitors as blocking capacitors. These can have a lot of leakage which will disturb the DC operating conditions of the opamp. Tantalum capacitors have lower leakage than electrolytics.
Also, some opamps just have open bases of transistors as their inputs. The LM324 is one of these and it must have appropriate resistance to the negative rail before it can work. If this resistance is accidental leakage of a capacitor, it may be temperature dependent.