The problem is, we know what we're made of, so why shouldn't this be the key to *some* life forms as well? Since we do not know that life can be made of sulfuric acid, we do not look for that, as with what we know, it's likely improbable.
Since there is an infinite combination of elements, and with the recent discovery of dust acting like it is alive in the interstellar medium, there are most likely life forms made of sulfuric acid, at least somewhere.
There is also the possibility of life thriving within a star, given it needs that much energy. However, chemical bonds tend to break down at that temperature. Given these, there is a maximum temperature for life to exist, but not a lowest one, other than absolute zero.
More likely, there will be silicon and arsenic based life, the latter already confirmed. We tested these because groups on the periodic table have similar chemical characteristics.
Since arsenic can become bacteria, I would not be surprised if there was a planet with intelligent life and the life being arsenic. However, there isn't that much arsenic, so it would be hard to find a region with enough arsenic to make an entire planet of life.
Silicon, although with its similarities to carbon, does not mean that it can process oxygen. There is a possibility, though, of silicon being able to consume and produce different elements.
Don't be so quick to say life doesn't need heat. You don't know that. The following sentence does make sense though.
Life might not need heat, but then it would take tens, even hundreds of billions of years to develop. The balancing factor, though, is that in colder regions, a planet is calmer than if it is closer to the star providing heat.
Also, movement and all other processes are slower at colder temperatures.