The three-dimensional velocity and temperature fields surrounding an isolated thermal plume in a fluid with temperature-dependent viscosity are measured using Particle-Image Velocimetry and thermochromatic liquid crystals, respectively. The experimental conditions are relevant to a plume rising through the mantle. It is shown that while the velocity and the isotherm surrounding the plume can be used to visualize the plume, they do not reveal the finer details of its structure. However, by computing the Finite-Time Lyapunov Exponent fields from the velocity measurements, the material lines of the flow can be found, which clearly identify the shape of the plume head and characterize the behavior of the flow along the plume stem. It is shown that the vast majority of the material in the plume head has undergone significant stretching and originates from a wide region very low in the fluid domain, which is proposed as a contributing factor to the small-scale isotopic variability observed in ocean-island basalt regions. Lastly, the Finite-Time Lyapunov Exponent fields are used to calculate the steady state rise velocity of the thermal plume, which is found to scale linearly with the Rayleigh number, in contrast to some previous work. The possible cause and the significance of these conflicting results are discussed, and it is suggested that the scaling relationship may be affected by the temperature-dependence of the fluid viscosity in the current work.