You can store Diet Standards Vegan Prenatal DHA Softgels at room temperature, but I highly recommend storing them in the refrigerator instead.
Any polyunsaturated fatty acid stores best at lower temperatures. If you look in my fridge, I've got Flaxseed Oil, Prenatal DHA, Olive Oil, and even Avocado Oil all refrigerated. Of course the Olive Oil and Avocado oil need to be thawed before use. But the Prenatal DHA can be consumed straight from the refrigerator.
Oh, another cool tip. Try chewing the softgels. Not only is it way more fun than swallowing more pills, after a few times your body will recognize the calories in the oil and start to really enjoy the taste of them.