This actually contains two questions.
1) The sun seems brighter (more dazzling) if there is more scattering in the atmosphere. The sun would actually look very small to us in the sky if there were no atmosphere (it's the same angular size as the moon) and most of the brightness seen in the direction of the sun is from small deflection rayleigh scattering. This depends on the amount of water vapour in the atmosphere, but much more on small dust/ash/sand particles (which also produce bright red sunsets). You notice increase in scattering as haze − the blue of the sky is washed out, pale, and in the direction of the sun, you have this wide yellowish blinding blob of light. The opposite of this is a "sharp", intense blue color which feels much more clear.
2) The sun feels hotter. If we assume the sun altitude is the same, it still sometimes feels much hotter, while the brightness is the same. That's due to humidity: water absorbs IR and UV light, but not much in the visible range, so it intercepts a lot of radiation that you don't see but still carries energy (this is true even if there is no cloud cover). This is also one of the reasons why UV index varies (of course, in this case, the ozone layer also plays a role).