I don't know what the exact number for steel would be but I expect the thermal expansion of the bar will be something like 0.0006" per foot of bar per 10°F. A 36" bar would "grow" 0.018" or so with a 100°F temperature increase.
Depending on which book you look at it can be anywhere from 0.0005 to closer to 0.0012" per foot of bar per 10F - lets just stick with your value of 0.0006 /ft/10F for now.
I have done some temp measurements using an infrared detector and here is what I found.
On a 65F day a well lubed freshly sharpened chain chain reached ~120F in softwood and 175 F in hardwood. If the chain is blunt, lube is poor/limited or a zillion other things the temps will be higher. So your 100F estimate is pretty good.
I have measured the chain reaching a steady temp under steady cutting in about one minute while the bar takes about 10 minutes to reach a steady temp.
This explains why the chain can appear to be very loose very quickly and why it should not be hard tightened (unless required), after just one minute of running as the still thermally expanding bar acting on an already thermally expanded chain will just stretch it even further.
After about a minute of running the bar will still be cool and not have expanded much but the chain will have expanded to
2 (chain is twice as long as bar) x 0.018" = 0.036" for a 3 ft bar and 0.06" for a 5 ft bar
This does not sound like much but if you use a simple pythagorean model to calculate chain droop (see "x" in the diagram= SQRT(30.06^2-30^3) for a 5ft bar) from the bar the droop is around 0.6" for a 18" bar, 1.1" for a 3 ft bar, and 1.9" for a 5" bar!
Doubling the temp difference will not double the droop but increase it to 2.7" for a 5 ft bar but it's still easy to see why a blunt chain contributes to why chains come off especially in that first few minutes after it goes blunt from hitting something etc.
Now something else to watch out for when adjusting.
The bar is typically 10-15 F cooler than the chain but the bar takes 10 minutes to cool down whereas the chain cools down in about a minute. This means if you stop the saw to adjust the tension you should do it asap or else the chain will shrink and you won't get the tension right.
It doesn't always happen but it sure is nice to see theory and practice line up reasonably well