Quality will be affected in either storage place once the bottle is open, because oxygen allowed into the bottle after opening will accelerate conversion to acetic acid (the vinegary taste of bad wine). The process will be slower if it is kept in the refrigerator, but there will be a definite loss of quality in a few days.
You will not have this problem with box wine that comes in an airtight platic bag (inside the box). I have noticed no deterioration of box wine kept at room temperture for months after opening. The problem is that most premium or snob-appealing wines are not sold in boxes.
To answer your question, store it in the refrigerator and then allow it to warm up to the serving temperature you prefer, before you drink it. It will stay "good" a few days longer that way.
They sell special stoppers for removing the air from opened wine bottles during room temperature (or refrigerator) storage. You can find out more about them at Amazon.com: Vacu Vin Wine Saver Gift Pack, White: Kitchen & Housewares
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