  We study the effective action for finite-temperature D3-branes with an
electromagnetic field at weak and strong coupling. We call this action the
thermal DBI action. Comparing at low temperature the leading $T^4$ correction
for the thermal DBI action at weak and strong coupling we find that the $3/4$
factor well-known from the AdS/CFT correspondence extends to the case of
arbitrary electric and magnetic fields on the D3-brane. We investigate the
reason for this by taking the decoupling limit in both the open and the closed
string descriptions thus showing that the AdS/CFT correspondence extends to the
case of arbitrary constant electric and magnetic fields on the D3-brane.
