Under this heading we are interested in the effect of temperature (T)  
on the phenomenon of induced fermion number. When fermions interact 
at T=0,  
with fields having a "toplogical" configuration - for example, 
a soliton, a vortex, a monopole, a skyrmion....- it is well known 
that a fermion number is induced which is related to the spectral 
asymmetry of the relevant Dirac operator; mathematical results 
concerning index theorems relate the fermion number to the asymptotic 
topological properties of the background field. Less is known about 
what happens at non-zero T. In several cases, the fermion 
number is T-dependent but the dependence on the background field is 
still only via its asymptotic (topological) behaviour. Work 
by I.J.R.Aitchison and G.V.Dunne 
(Phys. Rev. Lett. 86 (2001) 1690-1693) provides an 
example in which the induced fermion number at finite T depends 
on the detailed shape of the background. The leading low-T terms 
are summed to all orders in the derivative expansion, leading to 
a simple result that can be interpreted physically as the different 
effect of the background on virtual pairs in the Dirac sea and on 
real particles in the thermal plasma.