Thermogravimetric analysis (TGA) was performed on six samples of pine wood, poplar sawdust and olive residue, and the kinetic parameters were evaluated by using isoconversional models. The hemicellulose, cellulose and lignin contents were also estimated using the Fraser–Suzuki deconvolution method. In addition, a range of thermodynamic parameters and combustion indices was calculated. Significant correlations were found between the kinetic, thermodynamic and combustion parameters. The ignition index showed an inverse relationship with the activation energy, whereas the burnout index correlated with enthalpy values for most samples. Higher heating rates during TGA increased ignition and combustion efficiencies but decreased combustion stability. Differences in behaviour were detected between the olive residues, which had a much higher lignin content (51.2–56.9%), and the woody biomass samples (24.2–29.2%). Moreover, the sample with the highest ash content also exhibited some distinctive characteristics, including the lowest high heating value and ignition index, coupled with the highest activation energy, indicating a less favourable combustion behaviour than the other samples. The particle size of the samples was also found to be critical for both combustion efficiency and safety.