The High-Luminosity upgrade of the Large Hadron Collider (HL-LHC) will increase the accelerator’s luminosity by a factor 10 beyond its original design value, giving rise to more collisions and generating an intense flow of debris. A new beam screen has been designed for the inner triplets that incorporates tungsten alloy blocks to shield the superconducting magnets and the 1.9 K superfluid helium bath from incoming radiation. These screens will operate between 60 K and 80 K and are designed to sustain a nominal head load of 15 Wm−1, over 10 times the nominal heat load for the original LHC design. Their overall new and more complex design requires them and their constituent parts to be characterised from a thermal performance standpoint. In this paper we describe the experimental parametric study carried out on two principal thermal components: a representative sample of the beam screen with a tungsten-based alloy block and thermal link and the supporting structure composed of an assembly of ceramic spheres and titanium springs. Results from both studies are shown and discussed regarding their impact on the baseline considerations for the thermal design of the beam screens.