With a constant-current, constant-voltage power supply, does the total length of the wire affect the heat produced per metre?
It depends if you power supply is operating in constant voltage or constant current mode.
\$P = V^2/R\$ or equivalently \$I^2R\$ and \$R = L\rho\$ where \$\rho\$ is the resistance per length of the wire and \$L\$ is the length of the wire.
In constant voltage mode, for power per length we have \$P/L = V^2/(L\rho)/L = V^2/(L^2\rho)\$ which is not independent of \$L\$.
In constant current mode, \$P/L = I^2\cdot L\rho/L = I^2\rho\$ which is independent of \$L\$.