Due to its relatively higher temperature, the air in a thermal expands and is squeezed upward by the denser air surrounding it, which then flows in beneath as the thermal rises. Visualize the flow as having a sort of torus, or doughnut shape with behavior similar to a smoke ring blown upward. (Elongated vertically, it becomes a column.) While the central core rises, the outer portion rolls downward and then curls back in toward the core. If the lift is strong enough, that outer, downward curl will still be rising in relation to the ambient air. If the lift is weak, expect sink there, especially on the downwind side.
Thermals also may actually accelerate and expand as they rise. Fortunately for us, a thermal that is small and feeble down low might be very powerful higher up, and so large that remaining in it requires only a shallow-banked turn, and therefore a smaller penalty for circling. This explains why lift is often easier to find and use as you climb higher. Individual thermals that grow toward each other aloft sometimes unite near their tops, like trees in a canopy forest.
Typically, a uniform band of altitude where the lift is strongest, or more prevalent lies near the top of the useful convective layer, sometimes just below cloud base. In ideal circumstances, a confident pilot may elect to cruise only in that band, intending not to climb above it or descend below it. Eliminating slow climbs in weaker lift can add many miles, and miles per hour, during a long flight.
The logical corollary to this is a greater likelihood of sink at lower altitudes, particularly in the strongest conditions. Any experienced soaring pilot can tell of getting too low on a fine thermal day and being shot down by broad areas of thermal sink.