  The NP-complete graph problem Cluster Editing seeks to transform a static
graph into a disjoint union of cliques by making the fewest possible edits to
the edges. We introduce a natural interpretation of this problem in temporal
graphs, whose edge sets change over time. This problem is NP-complete even when
restricted to temporal graphs whose underlying graph is a path, but we obtain
two polynomial-time algorithms for restricted cases. In the static setting, it
is well-known that a graph is a disjoint union of cliques if and only if it
contains no induced copy of $P_3$; we demonstrate that no general
characterisation involving sets of at most four vertices can exist in the
temporal setting, but obtain a complete characterisation involving forbidden
configurations on at most five vertices. This characterisation gives rise to an
FPT algorithm parameterised simultaneously by the permitted number of
modifications and the lifetime of the temporal graph.
