The picture is thought to have hung in Ms Boothroyd's office until her retirement, when she donated it to the Beacon Centre.
Painted by renowned artist Edna Lumb, the picture depicts a colliery in Yorkshire where Ms Boothroyd was born and she kept it in her office because it reminded her of her childhood.
The picture will go on sale at Fielding's Auctioneers in Stourbridge on Saturday April 26.
Fieldings picture consultant Bill Lacey said: "I expect the piece to fetch at least £300 in auction, but I hope it will raise much more as the funds are going to a very worthy cause."
Interested parties can bid for the painting by visiting www.fieldingsauctioneers.co.uk or by calling 01384 444141 for further details.