Etymology: 1200s, from Middle English caudel, which is tied to Latin caldum, hot drink.
Coddle ("to coddle an egg") could be a similar origin. Coddling refers to cooking in water just below the boiling point.
Similar beverages include posset (milk curdled with spiced wine or ale) and eggnog (eggs, milk, sugar, spices, and alcohol).
From the 1300s book Le Viander (translated by Terence Scully), a recipe for caudle is behind the cut.
1/2 cup water
1/2 cup white wine
3 egg yolks
Take the water and put it on the fire. Take the egg yolks and beat them. Add the wine to the egg yolks, and beat it some more. When the water boils, take it off the heat, and let it cool a bit, then add the wine mixture into the water, stirring it constantly with a whisk. Heat the combined mixture slowly. stirring constantly. When it starts to boil again, take off the heat, add a dash of salt, stir to dissolve the salt, and serve it forth.