"In the shade" isn't a defined, unambiguous condition. It depends on the cloud cover, time of day, reflection from the surroundings etc. Yes, the temperature would be higher because the light source is the blue sky in addition to / instead of direct sunlight, but it's a wide range up to, say, 10000K or so. It would have to be determined in each specific instance.
The standard illuminants are just mathematical models, used for standardization.