After two weeks of bottle conditioning at about 55-60°F (13-16°C), my beer is still a bit flat. I put a few in the fridge and after 2 days, they tasted just as flat. At this point, what should I do? Find a warmer location? Just be patient and wait another week? Put 'em in the fridge or leave 'em out? I'm still not clear on what part refrigeration plays in bottle conditioning.
Yeast work better at warmer temps, and at this point you want the yeast to ferment the priming and carb your beer. That means you should keep the beer around 70-75°F (21-24°C) while you're trying to carb it. Once it's carbed, putting it in the fridge will not only aid the dissolution of CO2 into the beer, but will also retard staling. At this point, your best bet is to keep the beer at room temp and be patient.
CO₂ solubility is a function of temperature. If you can force carbonate, temperature and pressure can be varied in relation to each other to obtain a particular level of carbonation (generally expressed in the number of volumes of CO₂ dissolved into the beer).
When you bottle-prime, you've added a fixed amount of sugar, which means a fixed amount of CO₂. Temperature will only vary how readily it stays dissolved. If cold and you open with a "pop", then when heated you'll get a "POP". But the temperature won't change how much CO₂ present overall. If it's not carbed warm, it'll be perceived as even less carbed cold.
Please detail your priming/bottle conditioning process. What style of beer? How long in primary? What was the FG? What was your bottling process? How much priming sugar? How did you introduce the priming sugar?