Electronic – Why does a rise in ambient temperature cause a base-voltage-biased grounded emitter stage to saturate

This is actually exercise 2.9 in Horrowitz and Hill 2nd Ed. which is posed as:

Verify that an \$8 ^\circ C\$ rise in ambient temperature will cause a base-voltage-biased grounded emitter stage to saturate, assuming that it was initially biased for \$V_C = 0.5 V_{CC}\$.

The section it appears in is talking about the shortcomings of the single-stage grounded emitter amplifier, and mentions three deficiencies:

(1) non-linearity such that the gain varies from 0 to a (negative) maximum due to the lack of an external resistor on the emitter

(2) a variation in input impedance \$Z_{in} = h_{fe}r_e = 25 h_{fe} / I_C\$ (for \$I_C\$ measured in mA and the 25 is 25mV which is an estimate for \$V_T\$ in the Ebers-Moll equation, \$h_{fe}\$ is the gain and \$r_e\$ is the internal resistance)

(3) the effect of temperature on biasing according to which \$V_{BE}\$ varies by about 2.1mV / \$^\circ C\$ for fixed \$I_C\$. Apparently \$I_S\$ (the saturation current of the transistor) is roughly proportional to \$1/T\$, such that for fixed \$V_{BE}\$ the collector current \$I_C\$ increases by a factor of 10 for a 30\$^\circ\$ rise in temperature.

It feels like the answer to the question is a trivial consequence of (3), but I'm struggling due to not really understanding the conditions of transistor saturation, and how the \$8^\circ\$ rise in temperature can cause saturation regardless of \$V_{CC}\$.