First I want to say that I have no experience with capacitors heating up, so this one may be obvious.
I've recently replaced a set of aluminium electrolytic capacitors on an ADSL modem. The original ones vented. They were rated at 105 °C, so I got some 105 °C (of same voltage rating) capacitors as a replacement. Unfortunately, I couldn't find capacitors of the same size, so the modem is now outside of its plastic case.
Anyway, I noticed that the capacitors are getting hot. This is first time I noticed something like that. All other capacitors I've touched were always cool, even when used on a warm PCB. So I'm getting 45.5 °C on the cap of the capacitors. The outside temperature is 27.8 °C. The temperature of the PCB itself (measured from an exposed, unpopulated, solder pad) is 35.7 °C.
I do understand that the capacitors should be able to take the temperature without any problems, but it still seems a bit too high to me.
So is it normal for capacitors to heat up this much? I was unable to determine exact properties of the original capacitors (and Google isn't familiar with inscriptions on them), so I got some "low-ESR" capacitors just in case.
UPDATE: The capacitors are rated at 25 V (working at 12 V) and have capacitance of \$470 \mu F\$. The modem was bought in 2008. and was working more or less continuously (with no more than two months downtime for that period) since then until a month ago.