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.