This paper is concerned with the thermal instabilities occurring in a horizontal duct which is submitted to a mixed convection phenomenon. If we consider that the physical signals have a deterministic aspect, the system will be assumed as following a non-linear dissipative dynamic leading to a chaotic state. This state will be characterized and the transition to turbulence brought to the fore. More, we show how the physical mechanisms, responsible for these instabilities, induce different evolution of the space phase trajectory in a cross-section. We restrict this study to a descriptive aspect of the thermal behaviour of this system.