While heating the soil in greenhouses, ground heat exchangers are used, as well as when accumulating heat in soil massifs for further use of heat by heat pumps, or when accumulating heat from solar collectors in heat accumulators. In such cases, a coolant moves in the heat exchangers, which will not freeze or boil, most often these are solutions polyethylene/ethylene glycol, which belong to nonlinear viscous fluids. In this work, the nonisothermal motion of a nonlinear-viscous fluid (within the framework of the Ostwald - de Ville model) in a flat channel with a given heat flow on the wall is investigated. A characteristic feature of the flow of such media is their high thermal sensitivity due to phase and structural transformations. Therefore, with a change in temperature, there is a sharp change in rheological properties. For a number of materials, for example, for polyethylene glycol (ethylene glycol) mixtures, for glycerol solutions, these changes can occur in a fairly narrow temperature range. The flow in a channel is considered, the length of which is much greater than the length of the hydrodynamic and thermal initial sections. The case is investigated when the temperature changes along the channel. Channels of arbitrary cross-section (and, in particular, rectangular and circular) are considered. The situation is analyzed when the temperature changes along the channel, and this change is rather weak in relation to the temperature change along the channel walls (in the transverse direction, that is, in the plane of symmetry). To describe the state of the system, the so-called state diagram (dependence of the temperature on the axis of symmetry of the channel on the heat flux).