In the edge plasma of magnetically confined devices such as tokamaks, the electron distribution is not necessarily Maxwellian, and may consist of a small number of electrons characterized by a hot temperature, Teh, with the bulk of the electrons at a colder temperature, Tec· In a strong magnetic field, there is no satisfactory theory for interpreting the IV characteristic above floating potential, and so usually only the high energy electrons in the distribution are used to deduce Te. It is shown, that the value of Te extracted from the Langmuir Probe characteristic in this way yields Teh, unless the hot component is extremely small. Langmuir Probes therefore tend to overestimate Te in magnetically confined devices. This effect may also be relevant to observations of (apparently) very low sheath heat transmission coefficients in tokamaks.