What are " temporal kinetics"?
Temporal kinetics does not refer to the kinetics of kinase phosphorylation reactions and, since it is not standard terminology, you likely wouldn’t find its meaning in any textbook.
The authors of the paper quoted in the question use the phrase temporal kinetics to describe the phosphorylation state of a proteome-wide selection of kinase substrates (ie phosphorylation sites in proteins) over time. The general idea is that since one kinase can phosphorylate many substrates, clustering substrates based on their temporal kinetics (ie the times at which they become phosphorylated or dephosphorylated) can help identify the kinase and signaling pathway involved.
Fig 6B in the paper (shown below), for example, illustrates how 3,178 phosphorylation sites can be clustered based on the time-course of their phosphorylation and/or dephosphorylation after treatment of mouse adipocytes with insulin. As discussed in the paper, each cluster can be associated with one or more kinases based on known kinase-substrate interactions.