The electric charge of a Dirac monopole at nonzero temperature

We study the effect of nonzero temperature on the induced electric charge around a Dirac monopole. While at zero temperature the charge is known to be proportional to a CP violating θ parameter, we find that at high temperature the charge is proportional to sin θ. Other features of the charge at nonzero temperature are discussed. We also compute the induced charge at nonzero temperature around an Aharonov-Bohm flux string in 2 + 1 dimensions and compare the result with an index theorem, and also with the electron-monopole problem in 3 + 1 dimensions.