Abstract
We study the response of a scalar thermal field to a δ-probe in the context of non-local ghost-free theories. In these theories a non-local form factor is inserted into the kinetic part of the action which does not introduce new poles. For the case of a static δ-potential we obtain an explicit expression for the thermal Hadamard function and use it for the calculation of the thermal fluctuations. We then demonstrate how the presence of non-locality modifies the amplitude of these fluctuations. Finally, we also discuss the fluctuation-dissipation theorem in the context of ghost-free quantum field theories at finite temperature.
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