It isn't unlikely that new life is forming. Some scientists believe that life was indeed started in the ocean. (Sealife)
This is also why we are investing time in exploring one of Jupiter's more known satellites, Europa. Scientists theorize that under the frozen ice on
Europa's surface may lie an liquid water ocean.
If new lifeforms were formed, they wouldn't stand a chance against the much better adapted lifeforms that are already on earth. The current lifeforms
took billions of years to evolve and are much more advanced than new ones.
Or due to the heat up, previously unkown lifeforms are emerging from the depths of the ocean. Not sure if water temp is rising, or if it is, rising a
great deal.
If the water temp is increasing, then it is plausible that deep sea life is able to survive longer in shallower water.
The evolutionary process goes on all around us constantly, but speeds up, slows down and generally adapts itself to the climate. Therefore I can
imagine that new life should be starting to evolve if the seas are starting to heat up, Who knows what will come next, but then again, we are not
fully aware of what is in the ocean at the moment!
At the macro level animals could become larger if it is easier for them to exist in warmer water. Some creatures unable to adapt fast enough would
perish I believe.
Would land animals take to the water more frequently too if water is warmer? Seems likely.