  We define the local acceleration and jerk of a relativistic brane in an
ambient spacetime, and construct from them a dimensionless parameter lambda
that must be small for an interpretation of brane acceleration as local Unruh
temperature. As examples, we discuss (i) open rotating branes, for which
lambda>1 (ii) closed spherical branes expanding in Minkowski spacetime, for
which lambda=0 when the worldvolume is either an Einstein static universe or de
Sitter space, in which case the brane temperature equals the Gibbons-Hawking
temperature, (iii) closed spherical branes in anti-de Sitter spacetime, for
which a maximally symmetric worldvolume is anti-de Sitter, Minkowski or de
Sitter according to whether the magnitude of the brane acceleration is less
than, equal to or greater than a `critical' value, and (iv) the BTZ black hole,
viewed as a membrane.
