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It was recently proposed that there is a phase in thermal QCD (IR phase) at temperatures well above the chiral crossover, featuring elements of scale invariance in the infrared (IR). Here, we study the effective spatial dimensions d_IR of Dirac low-energy modes in this phase, in the context of pure-glue QCD. Our d_IR is based on the scaling of mode support toward thermodynamic limit, and hence is an IR probe. Ordinary extended modes, such as those at high energy, have d_IR=3. We find d_IR less then 3 in the spectral range whose lower edge coincides with λ_I
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