> 
> Yes, in a vacuum.  In air or with some other material contact, you need
> to include the conduction of heat too.
> 
And there can be a strong difference: Once I was experimenting with 
tungsten wires as an electron emitter. Under vacuum (10^-9mbar) you could 
push a current of about 4 amps to get a bright yellow glow - and an 
accordingly strong emission of electrons. OOC I put the same wire in air, 
connected to a lab power source driving a constant current of 4 A. 
Result: only a faint red glow. And when you blew air past the wire -just 
a little- it would stop glowing. And since the resistivity of metals is 
proportional to the temperature, you could observe the cooling also on 
the voltage meter of the power source. This setup can be used to measure 
gas flows, and a similar setup is actually used in mass flow controllers.

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