The 24-year-old's initial short-term loan move from National League side Guiseley AFC has been upgraded to run until the conclusion of the campaign.
Thompson netted his first league goal in United colours against Gainsborough Trinity on New Year's Day to add to an impressive portfolio of performances since arriving on loan in mid-November.
He also has two Lincolnshire Senior Cup goals - both scored against Gainsborough - to his name during his opening nine appearances in amber and black.