There currently are a variety of options to travel by night train from Hämeenlinna (Finland) to Rovaniemi (Finland), taking between approximately 9 and 12 hours: Namely the Yöjuna 265, the Yöjuna 267 and the Yöjuna 273. These lines are operated by VR.
VR, Finland's national railway operator, runs passenger trains throughout the country, including overnight services to northern Finland.