No one was injured, however the wall was damaged at the building in Glasgow.
The blazes have been set in the Sanquhar and Kelloholm areas of Dumfries and Galloway over the past few weeks.
The 26-year-old has been arrested over the alleged incident in Kilmarnock on April 10.
The blaze was extinguished by the Scottish Fire and Rescue Service and no-one was injured as a result of the incident.
The two family pets were injured in the 'reckless and cruel' incident in Peterhead on Thursday.