First order of business for any life that might arise there is to NOT catch the wind and NOT get in the flow.
Here on Earth, life gets its energy from soaking up solar energy, or from eating things that have been soaking up solar energy, or from eating things which have eaten things which.... you get the idea. The sole exception is at deep-sea geothermal vents, where you can pick up energy from the thermal gradient. On Gliese 581g, there's huge amounts of energy to be picked up just from the constant flow of energy from hot side to cold side, so I'd expect lifeforms to somehow be tapping into that.
On the other hand, if there's both sufficient water AND enough air for life as we know it on our planet's surface (excluding the extremeophiles like the flora living in Grand Prismatic Spring for the moment), the terminator wouldn't be nearly as clear as it is on Mercury, which has no atmosphere. Oceans of air and water would help to distribute heat throughout the world, much like they do here on Earth.
Given an earth-like atmosphere, the wind at the terminator would be a fairly constant 20mph from the sunward side to the shadowed side. Elsewhere, it would be slower. The upper atmosphere would circulate much faster than the rotational period of the planet, spreading the heat out pretty evenly over the planet.
Given an earth atmosphere, and the same heat from the sun as the earth, it would be about 25F on the shadow side pole, and 135F on the light side pole.
Of course, tectonics on a tidally locked planet are another thing, and if its surface has fused its atmosphere is probably chock full of H2SO4.