•Texture of homemade fruit beverages depends on temperature.•Beverages stability against sedimentation of fruit pulp was affected by temperature increase.•Information on the strength of microstructure at rest can be obtained from the activation energy approach. Fresh fruit beverages are a tasty way to follow the recommendations of World Health Organization. A study on the rheological behaviour of water-based and milk-based fruit beverages with emphasis on the temperature effect was made. The power law model adjusted data of apparent viscosity. The flow index of each beverage was practically constant with temperature variation. Then, one could discuss the variation with temperature of the consistency index. This parameter decreased around 40% in both cases in the temperature interval 5–30 °C. The stability of beverages against the sedimentation of the fruit pulp was clearly affected by the increase of temperature. Viscoelastic moduli were obtained in the linear region. Temperature dependency of both moduli was described in the interval 5–30 °C. The activation energy for linear viscoelastic flow was slightly higher than the activation energy for viscous flow. This result was interpreted as an indication of the strength of the microstructure-at-rest.