Pyromania is described in DSM-5 as a disorder in which an individual engages in repeated purposeful firesetting, as a means of achieving pleasure, gratification, or relief when setting fires or when witnessing or participating in their aftermath, and where other diagnoses and alternative motivations (such as vengeance or delusions) do not offer a better explanation for the behaviour (1). Pyromania is described very similarly in ICD-10 (2).
Sources: 1. American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC. (p.476).
2. ICD-10 Version:2016: Retrieved April 04, 2017: http://apps.who.int/classifications/icd10/browse/2016/en#/F06.7