The sun emits radiation close to black body radiation of a temperature of approximately 5800K. This radiation is electromagnetic radiation spanning the entire known range of energies. The intensity of some wavelengths is reduced due to absorption in the outer layers of the sun. We can, for instance, observe the spectral lines of hydrogen in the solar spectrum.
Electromagnetic radiation covers all wavelengths or frequencies if you prefer. Infrared, which we humans feel as heat, is also part of the spectrum. Therefore, the sun does emit heat. If the energy emitted by the sun is absorbed by an object, it has a high likelihood to transform into thermal energy, often after an excitation phase. This may then be interpreted as heat.
If you like to split hairs, electromagnetic radiation is not just heat and there is a large difference between heat and energy. I am a bit of an energy enthusiast, so I never use the word heat to denote enthalpy. Heat is, after all, the energy quantity related to specific enthalpy changes.
The surface temperature of the sun is for all intents and purposes constant, even on the time span of a hundred years. There are known solar intensity cycles of 7, 30, and approximately 100 years. These have all coincided recently. The solar radiation is however strongly affected by the distance to earth, which changes with the seasons, and the occurence of solar spots, solar flares, and other effects in the corona.
I have purposely left out any effects relating to the earths atmosphere as they would require pages upon pages to explain.