As　cloud　computing　is　becoming　growingly　popular,　consumers＇　tasks　around　the　world　arrive　in　cloud　data　centers.　A　private　cloud　provider　aims　to　achieve　profit　maximization　by　intelligently　scheduling　tasks　while　guaranteeing　the　service　delay　bound　of　delay-tolerant　tasks.　However,　the　aperiodicity　of　arrival　tasks　brings　a　challenging　problem　of　how　to　dynamically　schedule　all　arrival　tasks　given　the　fact　that　the　capacity　of　a　private　cloud　provider　is　limited.　Previous　works　usually　provide　an　admission　control　to　intelligently　refuse　some　of　arrival　tasks.　Nevertheless,　this　will　decrease　the　throughput　of　a　private　cloud,　and　cause　revenue　loss.　This　paper　studies　the　problem　of　how　to　maximize　the　profit　of　a　private　cloud　in　hybrid　clouds　while　guaranteeing　the　service　delay　bound　of　delay-tolerant　tasks.　We　propose　a　profit　maximization　algorithm　(PMA)　to　discover　the　temporal　variation　of　prices　in　hybrid　clouds.　The　temporal　task　scheduling　provided　by　PMA　can　dynamically　schedule　all　arrival　tasks　to　execute　in　private　and　public　clouds.　The　sub　problem　in　each　iteration　of　PMA　is　solved　by　the　proposed　hybrid　heuristic　optimization　algorithm,　simulated　annealing　particle　swarm　optimization　(SAPSO).　Besides,　SAPSO　is　compared　with　existing　baseline　algorithms.　Extensive　simulation　experiments　demonstrate　that　the　proposed　method　can　greatly　increase　the　throughput　and　the　profit　of　a　private　cloud　while　guaranteeing　the　service　delay　bound.　Note　to　Practitioners-This　paper　aims　to　solve　the　problem　of　task　scheduling　for　a　private　cloud　in　hybrid　clouds.　The　aperiodicity　of　arrival　tasks　brings　a　challenge　of　maximizing　the　profit　of　a　private　cloud　provider　while　guaranteeing　the　service　delay　bound　of　delay-tolerant　tasks.　Existing　methods　usually　provide　an　admission　control　to　refuse　some　of　arrival　tasks　that　exceed　the　capacity　of　a　private　cloud.　This　paper　first　proposes　an　architecture　of　temporal　task　scheduling　in　hybrid　clouds.　Based　on　the　architecture,　a　PMA　algorithm　is　proposed　to　provide　temporal　task　scheduling　which　can　maximize　the　profit　of　a　private　cloud　by　intelligently　dispatching　arrival　tasks　to　execute　in　private　and　public　clouds　within　the　service　delay　bound.　Preliminary　simulation　experiments　show　that　the　proposed　temporal　task　scheduling　is　feasible　but　it　has　not　yet　been　implemented　in　real　hybrid　clouds.　In　future　research,　we　will　extend　this　work　to　incorporate　multiple　different　tasks　that　require　heterogeneous　resources　including　bandwidth　and　storage.