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In meteorology, the term thermal wind refers to a difference in wind at different altitudes (the vertical wind sheer) at a particular location due to the effects of certain characteristics, i.e., horizontal gradients of temperature and pressure, and the Coriolis force. The (ideal) winds produced by just these factors is termed a geostrophic wind; in the real world, there are additional factors such as topography. The wind is said to be thermal because of its dependence upon a temperature gradient.
Typically air is warmed more the nearer to the equator, the expanded warm air resulting in a higher pressure at any given altitude, and the greater the altitude, the greater this effect. The air tends to move horizontally from the high pressure area toward lower pressure, the greater the altitude, the harder the "push". The Coriolis force (apparently) turns the wind, such that a north-south difference in temperature (and pressure) leads to wind along an east/west line: on Earth, toward the east in cases where the air that's further from the equator is the cooler.
This wind model yields tractable equations describing such winds, but it represents just some of the force on actual air movement, in particular, ignoring friction with the surface (ground). However, in some portions of the world, i.e., where geometry makes the Coriolis effect pronounced, the factors in this model are significant and may accurately model actual weather. An atmosphere moving according to the model is said to be in geostrophic balance if they match the equation describing geostrophic wind, and in thermal wind balance if they match the equation describing thermal wind.
The jet stream, a high-velocity, high-altitude west-to-east wind is a result of thermal wind.