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It is well known that fighting a fire is a hard task. The Firefighter problemasks how to optimally deploy firefighters to defend the vertices of a graphfrom 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 theefforts of good natured civilians who slow the spread of a fire by maintainingfirebreaks when they are able. We will show that this help, althoughwell-intentioned, unfortunately makes the optimal deployment of firefighters aneven harder problem. To model this scenario we introduce the TemporalFirefighter problem, an extension of Firefighter to temporal graphs. We showthat Temporal Firefighter is also NP-Complete, and remains so on all but one ofthe underlying classes of graphs on which Firefighter is known to havepolynomial time solutions. This motivates us to explore making use of thetemporal structure of the graph in our search for tractability, and we concludeby presenting an FPT algorithm for Temporal Firefighter with respect to thetemporal graph parameter vertex-interval-membership-width.

Making Life More Confusing for Firefighters