Aluminium Electrolytic Caps do dissipate power .This can be significant when the ripple current is large leading to Ohmic heating due to the ESR .Reputable manufacturers do provide Ripple current information so self heating can be factored into the lifetime calculation.My question is Does the ESR change with temp ? If it has a pos tempco runaway is possible but paralleled devices will share .If the tempco is neg there is good overall thermal stability but there is the possibility of current hogging in the group leading to a cap failing while the others are fine .I have paralleled electros many times in order to get the total ESR down and never been punished.Has anybody had a bad experience?
As with many questions like this, the answer is: it depends.
At low frequencies aluminium electrolytic ESR is not affected much by temperature. Most manufacturers measure this at around 100-120Hz across the rated temperature range, and some choose to measure it as a dissipation factor (DF), which is the ratio between the ESR and the capacitive reactance. Typically you're looking a negative temperature coefficient of a fraction of a percentage point per degree C.
At high frequencies, however, ESR is much more heavily dependent on temperature. The standard measurement frequency seems to be 100kHz. For aluminium electrolytic capacitors you will find that the ESR decreases significantly as temperature increases. The ESR at the temperature limit is usually somewhere around a 40-70% of the rated ESR at standard room temperature. However, you should keep in mind that these capacitors have a much more extreme ESR response to cold, even when using parts rated down to -40C, which can still result in a hundred-fold or more increase in ESR at the lower temperature limit.
In both cases there is the potential for thermal runaway due to ESR dropping as temperature goes up, but in low frequency scenarios this is not usually a concern due to the very low coefficient. In higher frequencies this is more of a concern. It is possible to resolve runaway issues to some extent by using a series PTC thermistor with an inverse temperature curve to the capacitor, placed nearby the capacitor on the board for good thermal conductivity, essentially acting as a temperature-corrected ESR for the capacitor.
As a side note, aluminium polymer capacitors have a lower ESR in general, and as such are less prone to runaway heating as the percentage change doesn't map to such a large absolute change in resistance. This may be useful in some design scenarios.