  We extend the effective field theory treatment of the thermodynamics of small
compactified black holes to the case of charged black holes. The relevant
thermodynamic quantities are computed to second order in the parameter
\lambda\sim(r_0/L)^(d-3). We discuss how the addition of charge to a caged
black hole may delay the phase transition to a black string. In the extremal
limit, we construct an exact black hole solution which serves as a check for
our perturbative results. Finite size effects are also included through higher
order operators in the worldline action. We calculate how the thermodynamic
quantities are modified in the presence of these operators, and show they enter
beyond order \lambda^2 as in the uncharged case. Finally, we use the exact
solution to constrain the Wilson coefficients of the finite size operators in
the extremal limit.
