Spiral arms have been observed in nearly a dozen protoplanetary discs in near-infrared scattered light and recently also in the sub-millimetre continuum. While one of the most compelling explanations is that they are driven by planetary or stellar companions, in all but one cases such companions have not yet been detected and there is even ambiguity on whether the planet should be located inside or outside the spirals. Here we use 3D hydrodynamic simulations to study the morphology of spiral density waves launched by embedded planets taking into account the vertical temperature gradient, a natural consequence of stellar irradiation. Our simulations show that the pitch angle of the spirals in thermally stratified discs is the lowest in the disc mid-plane and increases towards the disc surface. We combine the hydrodynamic simulations with 3D radiative transfer calculations to predict that the pitch-angle of planetary spirals observed in the near-infrared is higher than in the sub-millimetre. We also find that in both cases the spirals converge towards the planet. This provides a new powerful observational method to determine if the perturbing planet is inside our outside the spirals, as well as map the thermal stratification of the disc.
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