The evolution of the magnetization distribution with the temperature is investigated in a wide range (0-500K) in bilayers F
1/F
2 corresponding to a TbFeCo or DyFeCo layer F
1 with perpendicular anisotropy exchange-coupled with a planar layer (F
2) with low (GdFe and GdFeCo) or large (GdCo) in-plane anisotropy. The temperature dependences of the magnetic parameters (magnetization, uniaxial anisotropy, exchange constant) are first determined in the layers F
1 and F
2 from the mean field theory. In a second step the evolutions with the temperature of the magnetization distributions are obtained from a micromagnetic model using a non-continuous model of the magnetization. A re-orientation of the magnetization from in-plane to normal to the film F
2 is stimulated at a switching temperature
TS2 which depends strongly on the magnetic parameters (magnetization, effective anisotropy) of the planar layer. The extension of the analysis from ECDL (F
1/F
2) to ECTL (F
1/F
2/F
3) with two in-plane magnetic layers F
2 and F
3 shows the possibility to induce sequential phase transitions at different switching temperatures
TS2 and
TS3 with a dynamic expansion of the transition in the capping layer F
3 when
TS3>
TS2.
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