Temperature of Earth if tidal locked with the Sun? Assume the Earth somehow stopped spinning once every ~24 hours, and instead started rotating at ~365 days per rotation, so it effectively would end up being tidal locked with the Sun.  In this scenario, the same side of the Earth would always be facing the Sun, and the opposite side of the Earth would always be in darkness.  Disregard all sorts of cataclysmic events that would transpire if something like this happened.  

I think it would be safe to assume that life as we know it would quickly cease to exist except on the very edges of the day/night, but what would the approximate temperature stabilize at both on the point on the Earth directly facing the Sun, and a point on the surface of the Earth exactly away from the Sun?
That's very, very difficult to answer with a lot of if's. If the earth had no atmosphere it would be 255K-277K (-18-3°C) on the day side and a lot colder on the nightside. But if we include the atmosphere into our calculations we can get widely differing results.

For the sake of simplicity let's assume that earth tidal locks and nothing else happens. No change of atmosphere because many plants die or human population and therefore CO2 emmissions go down or something like this.

In this case I guess that the temperature would stay about the same. While one side of the earth enjoys permanent sunlight, the air on this side heats up and therefore rise to higher layers of the atmosphere. Cooler air from the other side of the earth streams in and the hot air in exchange streams to the cooler side where it cools down and returns to the bright side. So while one side of the earth is permanently sunny it is also permanently cooled down by air from the other side.

The dark side would not cool out because it is permanently heated by the hot air from the sunny side.

On the whole we would live on a very windy planet. But thats it.