Q: Is there any reasoning behind making capacitors go to 105°C? Electrolytic capacitors are often rated -40°C to +105°C. I've always wondered about the extra 5°C. This also seems to be the temperature range for some types of microcontrollers, and is marketed as an "extended temperature range", although in reality extended usually goes to +125°C. 
Is there any particular reason for this temperature - was it chosen to be 5.0161°C above the boiling point of water at 1 atm (99.9839°C or 100°C), or is there another reason?
Curiosity question - not going to be running any components at 105°C any time soon!

A: I can't say for certain how it started, but it's right in between the two MIL-PRF temperature ratings (85C and 125C, see MIL-PRF-39018, section 6.1 ). As a standard rule, aluminum electrolytics double their lifespan for each 10C drop in operating temperature, so it may be a convenient middle ground used for industrial and high performance consumer products.
I suspect Mike's correct in stating that the electrolyte chemistry has something to do with it and I would guess that improvements over time have made it more economical to produce 105C rated capacitors.
For further reading I'd suggest Cornell Dubilier's excellent application guide for electrolytic capacitors. They mention a connection between maximum rated temperature and total capacitance that implies that lower rated capacitors will likely be smaller than their higher rated counterparts. Extending the low end of the temperature range is possible but with a rapidly rising ESR.

A: It probably originates from the temperature that it's practical to make them work reliably due to the fluids used.
