As I was watching Tom Mueller describe the Merlin engine, he said that the RP-1 propellant is pumped through ribs in the nozzle to regeneratively cool the engine. Also, a video about Copenhagen suborbital's TM65 rocket engine shows how the alcohol fuel is used to cool the engine. Since both of these engines use liquid oxygen as their oxidizer, why would they use the fuel to cool the engine. Why not use the very cold liquified oxygen instead of the room temperature hydrocarbon fuels?
Whatever you use as a coolant will become hot. Hot oxygen will
(a) vaporize, making the plumbing somewhat more difficult, and (b) react with and erode (or maybe even ignite) the cooling channels, unless they're made of special materials.
The specific heat capacity of the fuel is higher than that of the liquid oxygen at the operating temperature/pressure, hence for the same rate of flow, using the fuel cools better ... and apart from any of the above-mentioned liquid/vapour/pressure issues.
The operating temperature range when using kerosene / RP-1 is also much greater than if using LOX.
As per my comment above, any "coolant" is not used because it's intrinsically cold, but because it can transport heat effectively in the required region at the required temperature range.