I note that in the midlands of England Caldwell and Chadwell seem almost to be synonomous. Chad or Caed was an early bishop and saint of Mercia. His cathedral was at Litchfield. In the midlands wells were venerated from antiquity until recent times and St Chad had a well at his cathedral which was visited by pilgrims. Chaud is hot in French and I think that Chaud-well Cold-well must have been hilarious for the Normans (if they took the trouble to learn English).