In order to make this world habitable, it needs to have low amounts of greenhouse-positive gases in its atmosphere (such as carbon dioxide or methane), potentially high amounts of greenhouse negative gases (such as sulphur dioxide), and higher albedo.
Since the OP doesn't want a hazy atmosphere with high sulphates, it's basically going to come down to low carbon dioxide and higher albedo. A little sulphate in the atmosphere may be acceptable.
As the temperature of this world rises, the OP's large seas are going to experience higher evaporation, which will lead to increased cloudiness, thus increasing albedo. As long as global warming doesn't proceed too far, this should be acceptable.
Since this world has greater insolation by definition, it may be that the vegetation has evolved to absorb only the necessary wavelengths of light, and reflect other wavelengths more than terrestrial plants do. This would serve to increase the world's albedo in vegetated areas.
The world could also have large areas of highlands near the equator that are high enough that they care covered with snow and ice, which also have a high albedo. The OP's map appears to show just such white highlands. In arid lowland areas, salt flats also have a high albedo.
Water is reflective when there is a low angle of incidence between the surface of the water and the light, such as occurs near sunrise and sunset, though it becomes lower in the middle of the day. However sea-foam also has a higher albedo, so another way of ensuring that this world's albedo remains high is to introduce organic compounds into the water that increase the amount and longevity of foaming in choppy seas, such as proteins and lipids.
So, with the right combination of airborn sulphur dioxide, low carbon dioxide, equatorial ice and snow coverage, cloudiness, reflective plants and concentration of organics in sea water, this world could easily have a sufficiently high albedo and low amount of greenhouse-positive gases to have an earthlike temperature.
As to how it evolved, high amounts of sulphur dioxide and a position further away from the star early in its history, followed by inwards migration as the amount of oxygen rose and greenhouse gases fell as a result of the processes of life could account for this without ending up with a venus-like world.