A　growing　number　of　global　companies　select　Green　Data　Centers　(GDCs)　to　manage　their　delay-constrained　applications.　The　fast　growth　of　users＇　tasks　dramatically　increases　the　energy　consumed　by　GDCs　owned　by　a　company,　e.g.,　Google　and　Amazon.　The　random　nature　of　tasks　brings　a　big　challenge　of　scheduling　tasks　of　each　application　with　limited　infrastructure　resources　of　GDCs.　Therefore,　hybrid　cloud　is　widely　employed　to　smartly　outsource　some　tasks　to　public　clouds.　However,　the　temporal　variation　in　many　factors　including　revenue,　price　of　power　grid,　solar　irradiance,　wind　speed,　price　of　public　clouds　makes　it　challenging　to　schedule　all　tasks　of　each　application　in　a　cost-effective　way　while　strictly　meeting　their　expected　delay　constraints.　This　work　proposes　a　temporal　task　scheduling　algorithm　investigating　the　temporal　variation　in　green　hybrid　cloud　to　schedule　all　tasks　within　their　delay　constraints.　Besides,　it　explicitly　presents　a　mathematical　equation　of　service　rates　and　task　refusal.　The　maximization　problem　is　formulated　and　tackled　by　the　proposed　hybrid　optimization　algorithm　called　Genetic　Simulated-annealing-based　particle　swarm　optimization.　Trace-driven　experiments　demonstrate　that　larger　profit　are　achieved　than　several　existing　scheduling　algorithms.