In Internet routing between autonomous systems which are interconnected in multiple locations, hot-potato routing is the practice of passing traffic off to another autonomous system as quickly as possible, thus using their network for wide-area transit.
Cold-potato routing is the opposite, where the originating autonomous system internally forwards the packet until it is as near to the destination as possible.
[1] Cold-potato routing (or "best exit routing")[2] on the other hand, requires more work from the source network, but keeps traffic under its control for longer, allowing it to offer a higher end-to-end quality of service to its users.
[1] It is prone to misconfiguration as well as poor coordination between two networks, which can result in unnecessarily circuitous paths.
[2] Routing behavior can be influenced using two BGP "knobs": multi-exit discriminator (MED) and local preference.