I just finished fermenting a brew and I forgot to remove the blow off tube which is a tube sitting in a 500 ml bottle of water. So when I started sucking beer out of my fermenter, I sucked all the water from the bottle. I decided to carbonate one of the 2 kegs at 2'C and store the other keg at 16'C. My question is: will these beers be contaminated?
Maybe, but probably not. Several things are working against contamination post-fermentation.
Was your blowoff tube pumping krausen into the water or just basically operating as an extended airlock? If it was pumping krausen that increases the chances of something growing in the water, but does not necessarily mean it will continue to grow in the keg. If it was just an extended airlock, then the only thing that went into the water was CO2. Even IF something was growing in the water, it would have had to produce off-flavors BEFORE going into your beer since due to the reasons above, it shouldn't continue growing.
Sure water sitting at room temp for 10 days could grow something, but generally sugar or something else is required for bad stuff to grow since they need something to eat. Bacteria can't just eat water. Given that this was also in a fermentation fridge (enclosed space) for the 10 days, it is even less likely that something landed in there and started to grow so I'd bet that you are perfectly fine with just very slightly diluted beer.
Again, the fact that your beer had alcohol and hops in it at the time the water was added will prevent almost anything else from growing in it. The biggest risk for contamination is pre-fermentation, not post. Like another comment said, yeast doesn't eat bacteria. Yeast only eats sugar. Chilling the beer causes the yeast to go dormant and settle out of the beer at the bottom so yes it stops working, but it wasn't "eating" the bacteria in the first place.
Yeast outcompetes other bad stuff in your beer simply because it reproduces so fast in wort. When you start fermentation, I guarantee there is contaminating bacteria in there no matter how good your sanitization practices are. The yeast just goes to work immediately and outcompetes the bad stuff, producing alcohol as a byproduct which in turn kills the bad stuff. Hopefully this clarifies things.
Depends on what bugs were in the water and whether they can reproduce fast enough to flavour the beer before your drink it.
My advice is to keep the beer as cold as you can to limit microbe growth, and drink it quickly. The beer stored at 16 C is much more at risk because the elevated temperature will accelerate microbe growth. If you can keep both kegs close to freezing, that's optimal.