I decided that it was time to run a test of what happens to the ESR of an electrolytic capacitor over temperature. As always, there were a few too many surprises. The idea was to test electrolytics that might actually be used in a computer and which had a history of failing.
I went to considerable trouble to make sure that the lead and contact resistance did not contribute any errors. The wires were silver plated and everything possible was soldered. In order to "zero out" the lead resistance, I crossed the capacitor leads and used pliers to short them. After some testing at room temperature, I found it to be highly repeatable. Test setup: Each run took about 30 minutes.
I ran temp tests on 4 different caps. Cap A = 1800 uf 6.3VDC. New. 105C. Purchased on eBay. Cap B = 2200 uf 10VDC. 105C. Removed from Dell with bulging top. Cap C = 1000 uf 6.3VDC. New. 105C. Unknown origin. Cap D = 0.22uf 50VDC. New. 85C. Unknown origin.
Spreadsheet with test results and graphs:
Cap A provided the initial surprise. The ESR was so low that the ESR meter reading was a constant 0.03 ohms above 40C. I would guess(tm) that this is a problem with the meter except that the meter reads my nichrome test wire, with less then 0.03 ohms quite nicely.
Cap B is a known defective capacitor with a bulging top that had not quite blown open yet (i.e. no leaks). The starting ESR is well above normal. This produced almost a 10:1 decrease in ESR as Phil Allison predicted.
Cap C was my attempt to find a cap that would give reasonable ESR values that would not produce the same lower limit problem as Cap A. It was better, but also hit bottom at 0.03 ohm. It's difficult to tell from the curve, but extrapolating from the starting values, it might have produced a 10:1 decrease in ESR if the meter had cooperated.
Cap D was another attempt to get reasonable ESR values and which produced another surprise: Since the ESR was well above the previous attempts, I would have expected another 10:1 decrease in ESR. Instead, it only decreased about 1.5:1. This suggests that higher voltage electrolytics have a more constant ESR, but more testing will be needed to verify that guess.
So, Phil is mostly correct. ESR does drop 10:1 in some electrolytic capacitors. Since power dissipation is directly proportional to the ESR (assuming a constant ripple current), a typical motherboard electrolytic capacitor will internally dissipate about 1/10th the power at maximum temperature as it would at room temperature. This explains an odd phenomenon that I've seen on computers with bulging caps on the motherboard. They'll sometimes run just fine when hot, but refuse to turn on function if allowed to cool. Also, I haven't seen any of this in the capacitor lifetime calculations.