Heat could be an issue, but you're doing the right thing with shading it partially. The soil in the picture looks somewhat damp - like it was watered recently, not like it needs to be watered again.
Someone suggested elsewhere that shading the pots to keep the soil cooler even when the plant tops are in the sun can help when growing in containers. I am not a container expert, but that seems like a good idea with something like parsely that doesn't like the heat so much. A larger pot would also help keep the soil cool.