Variation of the amplifier input impedance by the temperature
If you consider just a BJT in common-emitter configuration, the simplest expression of low-frequency input impedance is just \$r_{\pi}\$, which is \$\frac {V_T}{I_B}\$, where \$V_T\$ = \$\frac {kT}{Q}\$, so it's proportional to absolute temperature (PTAT). 

If you want it in terms of \$I_C\$, then the low frequency current gain dependency on temperature comes into play, and it's not a simple equation, and not necessarily even monotonic with temperature.