During my current physical I asked my doctor the reason for my persistent shin pain. Her opinion was that running can take a toll on various parts of the body, particularly the leg joints. She suggested that swimming is a life-long exercise and very safe for the body. The low impact nature of swimming is apparent, but question is, is there a difference whether I swim in cold water vs hot. Our local Y has 2 pools, one substantially warmer than the other.
If you are young and you have no past injuries to your knee ligaments, I suggest you don't give up running but rather focus on a better running technique, lowering your mileage for some time, changing your program or even trying different shoes instead. Medical doctors who aren't specially devoted to sport medicine are usually prone to sending you to swim at the very first sign of any discomfort. I do love swimming but I hate that attitude that arises from ignorance.
Do an internet search on "shin splints", it is a common annoyance among runners but it is not reason enough to quit unless you have really tried modifying another variables. By simply inserting extra rest days among runs your problem might be over. Or, as said, change shoes.
Besides that, swimming is not problem-free. Not for your knees. Google for "breaststroke knee" or "swimmer knee".
The last MD who told me to swim was a young but really obese guy with obviously no idea of sports. Many of them say blindly the same swimming-is-safe crap as a universal true for every problem. But no sport is 100% problem-free. The best sport for you is that one with the ability to motivate you and keep you engaged for years.
Swimming is generally considered a "safe" exercise, because it is low impact, so less wear and tear on the body. It is also a full body sport, which makes it better than other low impact alternatives such as cycling, where you don't get much upper body workout.
However, as have been pointed out in comments, you can still sustain injury if you swim with poor form, or use pool accessories (such as swim hand paddles) that are not correctly sized/used. Both of these can lead to stress and overuse injuries, especially if you are exercising at a higher intensity.
Every single sport has its own particular hazards. Swimming is usually a safer exercise, because it can easily be done at levels from very low exertion to high exertion, and it is very low impact (I count pushing off walls as an impact).
Shin splints are typically either an overuse injury, or an acute stress fracture type of thing. Shin splints are kind of a catch-all term for several things that can affect the lower leg. Lowering your mileage, getting new shoes that are matched to your running style, and lowering the intensity are all things you can do to help alleviate the pain. You may need to take a few weeks/months to let things heal before you restart running.
For your second question about temperature, it's personal preference. You may notice that you get fatigued faster in warmer water, and in any case, drink water. Yes, you will sweat when swimming, even in cold water.