Hi Jennifer,
actually I am not aware of a specific uranium-containing mineral with characteristic persistent luminescence. Yet, there might be a few minerals capable of persistent luminescence with uranyl-ions as activators. Calcite, gypsum or fluorite might show persistent luminescence with uranyl ions as activators - but as well other species.
The origin of persistent luminescence is linked to trap-states in the electronic structure of the material. Charge-carriers induced by illumination with e.g. UV-light get trapped and are slowly released by thermal energy at room temperature. Heating the material will lead to thermoluminescence.
For such a process to appear the material must allow for luminescence centers (activators) with a ground state - conduction band distance in the order of the energy of the exciting ligh (i.e. electrons are excited into the conduction band) and posess shallow trap states (i.e. stimulable by thermal energy at room temperature): this is a quite generic mechanism compatible to quite a handfull of minerals. If you look in literature you might search for "persistent luminescence", "afterglow", "phosphorescence", or similar.
My excuses for being of little help with respect to your initial question.
In case you are interested in more details or need some literature feel free to ask...
All the best, Martin