  We consider a spinor condensate of 87Rb atoms in its F=1 hyperfine state at
finite temperatures. Putting initially all atoms in m_F=0 component we find
that the system evolves into the state of thermal equilibrium. This state is
approached in a step-like process and when established it manifests itself in
distinguishable ways. The atoms in states m_F=+1 and m_F=-1 start to rotate in
opposite directions breaking the chiral symmetry and showing highly regular
spin textures. Also the coherence properties of the system changes
dramatically. Depending on the strength of spin-changing collisions the system
first enters the stage where the m_F=+1 and m_F=-1 spinor condensate components
periodically loose and recover their mutual coherence whereas their thermal
counterparts get completely dephased. For stronger spin changing collisions the
system enters the regime where also the strong coherence between other
components is built up.
