[Brian Running]

Heat is about current.

Actually, no. Drop a bazillion amps through 0 ohms and, no poof!
because no heat.

Actually, yes. Take a conductor with a high resistance, and put no
current through it, and poof! No heat.

Current is the flow of electrons,

Actually, no. Current is defined as the flow of charge.

Actually, yes. Charge is a measure of the quantity of electrons. A
coulomb is a definite quantity of electrons. When those electrons move,
it's current. Current is the flow of electrons.

and it is the
physical flow of electrons that causes the heat.

Actually, no. It is the thermal agitation of atoms and molecules
caused by the interruption of flow of current that is heat.

Actually, yes. It's the movement of the free electrons within the
conducting material that causes the heat.

Conductors and devices
are rated for current flow, not for power, because current is the actual
physical phenomenon that generates the heat.

Actually, no. Conductors are rated for current flow over a
certain length,

Actually, yes. They're rated by their cross-section, and it's dependent
upon the material they're made of.

Consider, as a practical example, the required
rating for a 100' extension cord carrying 15 amps, and a
15 amp fuse: the cross sections are radically different,
yet they have the same current carrying capacity.

And that would be a meaningful comparison if they were made of the same
conductor material. But they aren't.

The rise in temperature is determined by the rate in which
the heat is inserted into the system

From where? What's the source of the heat? Go ahead, say it: It's
the current flowing through the conductor.

And a quick check of the fundamental
units used for these calculations reveals it to be something
called "watts."

Because watts are a unit of power, which is what's used to measure the
work done or the heat dissipated. That doesn't change the fact that
it's electric current through a conductor that causes the heat in the
first place.

Current alone is NO determing factor of heat production. The
same current through two different systems having two different
resistances will produce two different amounts of heat.

It's the most basic factor in heat production in an electrical
conductor. Without current, there won't be any heat generated -- can't
get more fundamental than that.

Without a single exception, you will find the heat produced
to be a direct function of power, not of current.

That's just plain wrong. Power is determined by current. No current,
no power. Power measures the amount of heat generated, or work done,
but it's the electrical current that is fundamentally making the power
and causing the heat.