The thermometer reads, "cold as a brass monkey." This refers to the expression, "cold enough to freeze the balls off a brass monkey." A brass monkey was a brass tray, called a "monkey," used to hold cannonballs on warships in the 16th to 18th centuries. Supposedly, in very cold temperatures the "monkey" would contract, causing the balls to fall off. However, nearly all historians and etymologists now consider this story to be a myth.
The name Robespierre would also be the name of Wednesday Addams' classmate in The Addams Family TV series 20 years later.
The December calendar page hanging on the wall in the first scene is both current and accurate for when "Booby Hatched" first came out. The configuration of the dates match up with those of Dec. 1943. Since all the dates on this sheet except the last one have been "X"-ed out, it's fair to assume that the events in the cartoon are happening on Dec. 31, 1943. The actual release date of "Booby Hatched" was January 1, 1944.
Robespierre mentions the ongoing fuel oil shortage, which wartime cinema audiences would have appreciated. Gasoline, fuel oil, rubber tires, and many more everyday items were rationed for the ongoing war effort, with D Day just around the corner.
B.B. Wolf is likely short for Big Bad Wolf.