  It is well known that fighting a fire is a hard task. The Firefighter problem
asks how to optimally deploy firefighters to defend the vertices of a graph
from a fire. This problem is NP-Complete on all but a few classes of graphs.
Thankfully, firefighters do not have to work alone, and are often aided by the
efforts of good natured civilians who slow the spread of a fire by maintaining
firebreaks when they are able. We will show that this help, although
well-intentioned, unfortunately makes the optimal deployment of firefighters an
even harder problem. To model this scenario we introduce the Temporal
Firefighter problem, an extension of Firefighter to temporal graphs. We show
that Temporal Firefighter is also NP-Complete, and remains so on all but one of
the underlying classes of graphs on which Firefighter is known to have
polynomial time solutions. This motivates us to explore making use of the
temporal structure of the graph in our search for tractability, and we conclude
by presenting an FPT algorithm for Temporal Firefighter with respect to the
temporal graph parameter vertex-interval-membership-width.
