The battery has a fixed voltage V. If the total resistance in the circuit is R, then the current flowing through the circuit is:
<br />
I = \frac{V}{R}<br />
The total power released in the resistor is:
<br />
P = R \, I^{2} = R \, \frac{V^{2}}{R^{2}} = \frac{V^{2}}{R}<br />
Notice that the power is inversely proportional to the resistance. The maximum power will be released when the resistance is minimal. We cannot make the resistance in the circuit to be less than the internal resistance of the source. This happens when we connect the ends of the source by a wire with negligible resistance. This is called short-circuit. The keys and coins essentially create a short-circuit.
When you say the battery was red hot, I presume it was no more than 60 oC, since anything above that would melt or burn your clothes. The AAA batteries have dimensions 44.5 mm in length and 10.5 mm in diameter. This gives a surface area of the side equal to:
<br />
A = \pi \times 10.5 \, \textup{mm} \times 44.5 \, \textup{mm} = 1.47 \times 10^{3} \, \textup{mm}^{2} = 1.47 \times 10^{-3} \, \textup{m}^{2}<br />
According to Stefan's Law, the intensity of radiation is:
<br />
I = \sigma \, (T^{4} - T_{a}^{4})<br />
where T = 333 \, \textup{K} is the absolute temperature of the surface and T_{a} = 293 \, \textup{K} is the ambient temperature. Here, \sigma = 5.670400(40) \times 10^{-8} \, \textup{W} \, \textup{m}^{-2} \, \textup{K}^{-4} is the Stefan Boltzmann constant. From these figures, we get an intensity of:
<br />
I = 2.79 \times 10^{2} \, \frac{\textup{W}}{\textup{m}^{2}}<br />
The total radiated power is:
<br />
P = 0.41 \, \textup{W}<br />
A current of 0.41 \textup{W}/1.5 \, \textup{V} = 0.27 \, \textup{A} could supply this power and for this, the total resistance in the circuit has to be 1.5 \, \textup{V}/0.27 \, \textup{A} = 5.5 \, \Omega. This indeed corresponds to a short circuit.
