The intermittency of turbulent superfluid helium is explored systematically in a steady wake flow from 1.28 K up to T > 2.18K using a local anemometer. This temperature range spans relative densities of superfluid from 96% down to 0%, allowing to test numerical predictions of enhancement or depletion of intermittency at intermediate superfluid fractions. Using the so-called extended self-similarity method, scaling exponents of structure functions have been calculated. No evidence of temperature dependence is found on these scaling exponents in the upper part of the inertial cascade, where turbulence is well developed and fully resolved by the probe. This result supports the picture of a profound analogy between classical and quantum turbulence in their inertial range, including the violation of self-similarities associated with inertial-range intermittency.