PEN INSULIN storage

After installing insulin in an insulin-pen, do I have to take out the insulin after every shot (3 times a day) and store it in the fridge or can leave insulin in the pen?

I will use the insulin for 30 days and discard the remaining.

I got my pen yesterday, so trying to understand insulin storage. (last month I have used syringes and stored the VIAL in fridge)

Pens are room temp once they are first used. The unused should stored in fridge until time to switch to a new one. The package insert should explain so check it out or you can go the online site for the type of pen you are using.
If your work/life storage conditions are too hot or cold for the pen you can look at getting a frio case to carry it in.
BTW never leave insulin pen in the car as it can get too hot or too cold depending on outside conditions. Carrying a pen on your person usually is just fine.

Thank you for your response. I"ll store the unused as advised.

The manufacturer recommends storing at room temperature (below 77f) usually, once opened for 28 days. I usually keep them in the fridge anyway, and often use past 28 days with no problem.