"The plates are heated in three ways;— by radiation [radiant heat] from the fire and from the plate-warmer itself, by  reflection from the plate-warmer, and also by  conduction and communication from it [heat absorbed by the warmer]." [The London and Edinburgh philosophical magazine and journal of science, 1835]
"The common plate-warmer, which seldom does its work; and, to do so, must stand between the fire and the company, who are thus robbed of their comfort." [The Atheneum. Boston: 1827] For diners sitting too close to the fire, there were chair screens to protect their back, as I posted HERE
Kitchen plate warmers could be a wooden case
or a simple metal one, as seen at the Rock Run Mansion in Susquehanna State Park near Havre de Grace, Maryland:
One of a pair of japanned tin plate warmers which George Washington purchased in New York City, (in 1790 while President), is at Mount Vernon. More information about this item is on the Mount Vernon website HERE
Merchant's House Museum , NYC, shows the original japanned painting.