I take my pens straight from the fridge and put them right back. Warming and cooling cycles probably aren't good for the peptide. If you really want it at room temperature, skip the pen and just draw your dose from the vial then return the vial to the fridge.
After reading up I'm still unsure about the right way to handle a weekly shot from a pen kept in the fridge between uses. Some say let the mixed peptide reach room temperature before injecting, while others say keep it out of the fridge as briefly as possible so temperature swings don't speed up breakdown. That would mean injecting right after taking it out. What do others think and what do they actually do?