Dan:

I have used Tantalum Caps in quite a few projects and one of the applications
is the transient suppression capacitor across a 7805 etc. voltage regulator
that was running pretty much at full capacity 90% of the time therefore was
getting quite warm.  The tantalum cap was right next to the regulator/heat
sink and I never experienced any problems.  As far as I know that piece of
hardware (which was fabricated around 6 years ago) is still running with not
problems.  It is also inside a dustproof enclosure with NO ventilation, due
to some special requirements of the environment in the plant.

I hope this helps but as to the actual specs., I couldn't give you those.
Best thing to do there is to check the manufacturers sheets.

Randy A.