One-dimensional systems with short-range interactions cannot exhibit a long-range order at nonzero temperature. However, there are some particular one-dimensional models, such as the Ising-Heisenberg spin models with a variety of lattice geometries, which exhibit unexpected behavior similar to the discontinuous or continuous temperature-driven phase transition. Although these pseudo-transitions are not true temperature-driven transitions showing only abrupt changes or sharp peaks in thermodynamic quantities, they may be confused while interpreting experimental data. Here we consider the spin-\frac{1}{2} Ising-XYZ diamond chain in the regime when the model exhibits temperature-driven pseudo-transitions. We provide a detailed investigation of how this phenomenon occurs in several physical quantities, such as entropy, magnetization, specific heat, magnetic susceptibily, and correlation functions between distant spins that illustrates the properties of quasi-phases separated by pseudo-transitions. Inevitably, all correlation functions show the evidence of pseudo-transition. It is worth to mention that the correlation functions between distant spins have an extremely large correlation length at pseudo-critical temperature.