We studied the influence of annealing conditions on magnetic and thermal properties of Finemet-type alloys. The evolution of the Curie temperature, Tc, and the change of heat capacity in the vicinity of this magnetic transformation, ΔCp Tc, were investigated using Differential Scanning Calorimetry, DSC. Relaxation of atomic structure of amorphous phase during the annealing was accompanied by an increase in Tc and decrease in ΔCp Tc. Two relaxation processes with different mechanisms take place in amorphous state: topological ordering and chemical ordering. The study of the kinetics of relaxation process allows to estimate the apparent values of activation energy of both relaxation processes: 29 and 87 kJ/mol for ribbon, 37 and 112 kJ/mol for microwire. Precipitation of α-Fe nanocrystallites in amorphous phase leads to gradual degradation of the Tc peak. The Tc peak reduction is correlated to decrease of the amorphous phase as well as lowering of its magnetostriction. The influence of internal stress on the position and shape of the Curie peak was determined by comparing data for the ribbon-shaped alloys and glass coated microwires. Considerable magnetic softening and giant magnetoimpedance effect under heat treatment is observed in the studied Finemet-type microwires. Changes in magnetic properties after heating are associated with devitrification and stresses relaxation. We also study the influence of internal stresses induced by glass coating on the magnetic properties of as-prepared and annealed microwires. The results confirm the previously made conclusion that changes in the thermal and magnetic properties of Finemet-type alloys during heating are interrelated, since they are reflections of the fundamental characteristics of the material. © 2019 Elsevier B.V.