Yes, asphalt will initially be cooler, and take much longer to heat up than
a blade of grass. The blade of grass will reach equilbrium with its
surroundings rather quickly. The asphalt will take a long time to heat up
and hold a lot more heat than that blade of grass.
In the evening when it starts to cool down, the blade of grass will give off
its heat very quickly. The asphalt will continue giving off heat well into
the night. So... the grass will have less impact on night time temperatures