If it is a fuse, why would they put one in a simple nicad battery
pack
for a cordless phone?

You've never seen a guy put a nicad battery pack into his pocket along
with loose change and some keys, I take it :-). NiCads are very
capable of getting very hot when shorted out.

From your description as a cylindrical package it sounds like that may
be a Bel MQ or MS style package (page 1123 in current Digikey catalog.)

Tim.