If you use the entire bottle within a couple of weeks, room temperature is fine. However, if it takes you longer, you may want to refrigerate. Every bottle I've kept at room temperature (77*F) always ends up reporting lower values than what they actually are, this causes you to increase your Alk if you are not aware of this.
This has happened to me a couple times before I realized it was time to refrigerate. I would get to the end of the bottle, get low readings and increase my Alkalinity accordingly, the new bottle would come in and it would read way higher than the old bottle. I would then buy another new bottle with a different batch # and get the same results as the other new bottle, and the old bottle would still yield low numbers.
Now that I refrigerate the product, I get the same values (~0.1 difference) as my old refrigerated bottle versus a brand new bottle.