Should I soak my temporary or final denture in cleaning solution? (including one with a relined inner surface)

It depends on whether it has been relined. An ordinary denture can be soaked in denture cleaning solution to disinfect it, but a denture whose inner surface has been relined with a soft material can degrade or lift if soaked for long periods in a strong cleaner. Basic care is 1) cleaning it gently after meals under cool running water with dish detergent, 2) storing it in room-temperature water overnight, and 3) never using hot water or bleach, because of the risk of deformation. Whether cleaning solution can be used on a relined denture depends on the material, so we will confirm it at your visit.