With　increasingly　popular　GPS-equipped　mobile　devices　(e.g.,　smartphones,　tablets,　laptops),　massive　spatio-textual　data　has　been　outsourced　to　cloud　servers　for　storage　and　analysis　such　as　spatial　keyword　search.　However,　existing　privacy-preserving　spatial　keyword　query　schemes　only　support　coarse-grained　non-temporal　access　control　in　single　user　sharing　scenario,　which　does　not　scale　well　in　time-related　scenes　such　as　message　valid　period.　To　solve　the　above　issues,　we　propose　Privacy-preserving　Boolean　Range　Query　with　Temporal　access　control　in　mobile　computing　(PBRQ-T).　Specifically,　we　first　achieve　PBRQ　with　linear　search　complexity　using　the　adapted　Gray　code,　Bloom　filter,　and　Katz-Sahai-Waters　encryption.　Then,　we　provide　fine-grained　and　temporal　access　control　in　PBRQ　based　on　the　forward/backward　derivation　function　and　attribute-based　encryption,　where　PBRQ　is　executed　only　when　the　spatio-textual　data　is　accessible.　Finally,　an　enhanced　PBRQ-T　(i.e.,　PBRQ-T+)　with　faster-than-linear　search　complexity　is　proposed　by　constructing　a　Quadtree　index　structure.　Our　formal　security　analysis　shows　that　data　privacy　and　index　privacy　can　be　guaranteed　during　the　query　process.　Our　extensive　experiments　using　a　real-world　dataset　demonstrate　the　efficiency　and　feasibility　of　our　schemes.