Step 1: Recall the microscopic picture of a metallic conductor.
In a metal, free electrons move through a fixed lattice of positive ions. The number of free electrons is determined by the atomic structure (each metal atom contributes a fixed number).
Step 2: Analyse the effect of heating on resistivity.
When a conductor heats up, the lattice ions vibrate more vigorously. This increases the chance of collision for free electrons, so resistivity $\rho$ increases with temperature.
Conclusion: Resistivity changes.
Step 3: Analyse the effect on resistance.
Resistance $R = \rho L / A$. Since $\rho$ increases on heating, $R$ also increases (for constant geometry).
Conclusion: Resistance changes.
Step 4: Analyse the effect on drift speed.
Drift speed $v_d = I/(neA)$. For a constant battery voltage, as resistance rises, current $I$ falls. So drift speed also decreases.
Conclusion: Drift speed changes.
Step 5: Analyse the number of free electrons.
Each atom in the metal lattice contributes a fixed number of valence electrons. Heating increases thermal vibrations of ions but does not cause ionisation or recombination at the temperatures of ordinary resistors.
The free electron density (number per unit volume) remains essentially constant.
Conclusion: Number of free electrons does not change.
Step 6: State the answer.
\[
\boxed{\text{D: Number of free electrons}}
\]