In this work, functionally graded lanthanum magnesium hexaluminate (LaMgAl₁₁O₁₉)/yttria-stabilised zirconia (YSZ) thermal barrier coating (FG-TBC), in as-sprayed and laser-glazed conditions, were investigated for their thermal shock resistance and thermal insulation properties. Results were compared with those of a dual-layered coating of LaMgAl₁₁O₁₉ and YSZ (DC-TBC). Thermal shock tests at 1100 °C revealed that the as-sprayed FG-TBC had improved thermal stability, i.e., higher cycle lifetime than the as-sprayed DC-TBC due to its gradient architecture, which minimised stress concentration across its thickness. In contrast, DC-TBC spalled at the interface due to the difference in the coefficient of thermal expansion between the LaMgAl₁₁O₁₉ and YSZ layers. Laser glazing improved cycle lifetimes of both the types of coatings. Microstructural changes, mainly the formation of segmentation cracks in the laser-glazed surfaces, provided strain tolerance during thermal cycles. Infrared rapid heating of the coatings up to 1000 °C showed that the laser-glazed FG-TBC had better thermal insulation capability, as interlamellar pores entrapped gas and constrained heat transfer across its thickness. From the investigation, it is inferred that (i) FG-TBC has better thermal shock resistance and thermal insulation capability than DC-TBC and (ii) laser glazing can significantly enhance the overall thermal performance of the coatings. Laser-glazed FG-TBC provides the best heat management, and has good potential for applications that require effective heat management, such as in gas turbines.