The theft occurred at approximately 12.40am on Thursday, October 26.
Wiltshire Police said the thieves used malicious keyless entry to gain entry to the vehicle before driving it in the direction of Weston Lane, Winterslow.
Police noted a rise in keyless vehicle thefts earlier this year, with both Hampshire and Wiltshire Police releasing posts on social media in June announcing the increase.
Hampshire Police specifically noted a rise in the theft of keyless Ford Transit vans in Southampton, Eastleigh and the New Forest in July.
Police are now appealing to the public for help in their investigation of the Thursday, October 26 theft, asking anyone who may have seen the vehicle being driven on that morning or have dashcam footage of the vehicle being driven at that time to call 101 using crime reference number 54230113304.