Why do so many IC's have a max temp range of 125C? Is it due to packaging material tolerances, ie the black plastic enclosures and/or the bonding epoxy that holds the die to the package and/or something else?
All semi-conductor characteristics are affected by Boltzman statistics relating charge carrier densities with respect to temperature. The hotter it is the more intrinsic carriers are present, at some point the intrinsic carrier concentration gets so high that any doping (n-type vs. p-type) gets wiped out. That is at high temperatures.
A conductor has the characteristic that as you heat it, the carriers are more mobile and collide more and resistance goes up. A Semi-conductor has the characteristic that as you heat it up, more carriers are present and the resistance goes down.
So it's natural to see that there are limits. Why particularly those temperatures, I don't know, I'm sure some one will come up with the historical answer. However, it's very celar that some temperature must be selected, because if you design for a very broad temperature range then some other performance metric will be compromised, like speed or margins.
Designs are specified over what are called PVT corners, as in Process, Temperature and Voltage corner cases.
The military temperature range for operation of silicon integrated circuits (ICs or chips) is -55C to +125C, which is meant to ensure operation in virtually any field situation, with plenty of margin (125C is 25% hotter than the boiling point of water).
Other standard ranges for ICs are -40C to +125C for Automotive, -40C to +85C for Industrial, and 0C to +70C for Commercial (e.g. chips in TV sets). There are variations in these standards, for example some automotive devices may extend to +130C or higher, and high performance CPU chips in home computers may be limited to +55C.
A chip's packaging is chosen according to the chip's rated temperature range and is generally either plastic for lower temperature devices and ceramic for higher temperature. Ceramic packages also have superior sealing and may have provision for mating with an external heat sink to cool the package.
The silicon from which ICs are made has a limit beyond which heat generated by the chip's circuitry can't flow through the silicon and out of the chip fast enough to prevent permanent damage, regardless of external heat dissipation methods (heat sinks). The faster the clock signal for a digital chip such as a CPU, the more heat it generates because the clock signal spends more time in the transition region between high and low logic states. Clock transitions are the only time a typical digital circuit generates significant heat, so more heat is generated as the clock speed is increased. A typical upper limit for clock speed in silicon ICs is around 4 GHz (4,000 MHz) but some specialized devices can be clocked much faster.