We consider the possible formation of spin polarons in the double exch
ange model at finite temperatures. We show that the average size of a
spin polaron in this model increases as the temperature decreases. Bas
ed on this, we argue that the transition to the ferromagnetic phase in
the double-exchange model happens when the spin polarons start overla
pping. The effect of the external field is shown to reduce the effecti
ve temperature and thus to increase the size of the polarons. The theo
ry predicts a linear increase of T-c versus the applied external magne
tic field, a temperature dependence of the magnetic susceptibility abo
ve T-c that deviates from Curie-Weiss behavior, and an increase of T-c
as the electron/hole density increases.