Solar radiation is roughly 1 kilowatt per square meter. Human beings generate about 0.1 kilowatts. A good suit will try to reject as much of that kilowatt as possible. Also your dark side will radiate heat but the temperature differential is much lower.

Suits are insulating for a reason. You want to prevent heating on the sun side and prevent too much cooling on the space side. Your body is essentially encapsulated in a giant thermos.

Cooling is achieved using a recirculating cold water system that is good for a few hours of body heat. Water is initially cooled by the primary life support system of the spacecraft before an EVA. Pretty much it starts off pretty cold and slowly over time comes up to your body heat. Recent designs use evaporative cooling to re-cool the water.

Life support systems are so cool.

Absorbed light too but that's a bit easier to deal with and is why most things are white or reflective on the outside of anything in space that's not intentionally trying to absorb heat.