Thermalisation of single electron devices is of considerable current i
nterest because of its fundamental and practical consequences. We pres
ent experimental evidence of the effect of electrode volume and its sh
ape on thermal equilibration of small metallic islands for single elec
tron tunnelling. Heat transport between the conduction electrons and t
he lattice in a metal is commonly accepted to obey the proportional to
T-e(5)-T-0(5) law at low electron and lattice temperatures, T-e and T
-0, respectively. We have investigated the power law and found that it
obeys the proportional to T-5 law only for the smallest islands, and
in the majority of the cases considered, it rather follows a law propo
rtional to T-p where p <5. The thermal coupling can be improved by inc
reasing the volume of the island, but, upon increasing the surface are
a alone, the effective coupling constant is reduced indicating the pre
sence of local hot electrons.