Sir Henry Vane-Tempest, 2nd Baronet (25 January 1771 – 1 August 1813) was a British politician.
Vane-Tempest was the son and heir of Reverend Sir Henry Vane, 1st Baronet and his wife, Frances, née Tempest. He was Member of Parliament (MP) for the City of Durham from 1794 to 1800, replacing his uncle John Tempest from whom he inherited the Tempest estates in County Durham (notably Wynyard and Brancepeth) upon condition he adopt the name and arms of Tempest. He accepted the Chiltern Hundreds in 1800 before returning to Parliament as representative for the County Durham from 1807 until his death from apoplexy in 1813. He was appointed High Sheriff of Antrim in 1805.
Vane-Tempest inherited his father's baronetcy in 1794. He was appointed lieutenant-colonel of the Durham volunteer cavalry in early 1797. On 25 April 1799, he married Anne MacDonnell, 2nd Countess of Antrim and they had one child, Lady Frances Anne Vane-Tempest (1800–1865), who married Lord Charles Stewart (later Marquess of Londonderry). On his death the baronetcy became extinct. He is buried at Long Newton.
Vane-Tempest was a renowned sportsman of his day, owning the celebrated racehorse Hambletonian. In a match with Mr. Cookson's Diamond over the Beacon Course at Newmarket in 1799, Hambletonian won by a neck, Sir Henry having wagered 3,000 guineas on the outcome. The aftermath is the subject of George Stubbs' painting "Hambletonian Rubbing Down".