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In the paper the positivity problem of the model of an one dimensional heat transfer process is addressed. Such a problem has not been considered yet. The considered thermal process is described by the fractional order state equation, derived from parabolic heat equation with homogenous Neumann boundary conditions and distributed control and observation. The internal and external positivity of the model depend on heater and sensor location as well as the size of the model. It is proved that the external positivity of the considered syste