I'm not certain where I first heard of heating bricks to keep warm during traveling during the Regency period. It may have been in P&P variations. I know I've also heard of using them to keep feet warm in winter by placing them at the foot of beds.
I can't provide a specific reference for using heated bricks to keep travelers feet warm while riding in carriages.
Curiously, I did find several references for buying special heating bricks from online vendors.
Also curiously, the online Merriam-Webster dictionary does refer to heating bricks to keep warm under the definition for "heated." They apparently are not something new and after reading about them it seems logical to me that they would have been used in carriages by travelers.