The possibility of pion-pair formation in a hot pion gas, based on the
bosonic gap equation, is pointed out and discussed in detail. The cri
tical temperature for condensation of pion pairs (Evans-Rashid transit
ion) is determined as a function of the pion density. As for fermions,
this phase transition is signaled by the appearance of a pole in the
two-particle propagator, In Bose systems there exists a second, lower
critical temperature, associated with the appearance of the single-par
ticle condensate. Between the two critical temperatures the pion dispe
rsion relation changes from the usual quasiparticle dispersion to a Bo
goliubov-like dispersion relation at low momenta. This generalizes the
non-relativistic result for an attractive Bose gas by Evans et al. Po
ssible consequences for the inclusive pion spectra measured in heavy-i
on collisions at ultra-relativistic energies are discussed.