This kind of desk was very popular in prosperous homes in Europe during the 18th century and slowly disappeared during the 19th, with the gradual introduction of stoves and central heating.
In order to keep the feet and the calves exposed to the heat from the fire, the fire screen desk usually had the form of a miniature writing table or a tiny bureau à gradin, with just a few drawers beneath the desktop.
As its name indicates, it had a retractable fire screen in the back to protect the user's relatively exposed face from too much heat from the fireplace.
Their high form shielded the user's face from the heat of the flames while the open trestle mount at the bottom exposed the feet.
They were basically a smaller version of a French form called Secretaire en portefeuille.