Zinc does liberate hydrogen gas at room temperature when it comes in contact with dilute sulphuric acid, as it does with hydrochloric acid.
Zn + H2SO4 (dil) → ZnSO4 + H2
But when the metal is heated with concentrated sulphuric acid, the latter is reduced to sulphur dioxide.
Zn + 2H2SO4(conc) → ZnSO4 + SO2 + 2H2O
conc.H2SO4 acts as an oxidizing agent at high temperatures (hot conditions). The oxidation state of sulphur gets reduced from +6 (in H2SO4) to +4 (in SO2) in such types of redox reactions.