Does particle radiation heat the quartz block?
Yes, but not very much. The thermal conductivity from the block to the helium is very high, and the heating power of the radiation is quite small. Consequently the temperature rise is very small because the heat is conducted away as fast as it is deposited in the block. The actual rise depends on the details of the thermal grounding of the block, but in a conservative estimate, assuming all of the peak available energy of the radiation continuously heating the block, the temperature rise at the center should be no more than a few times 10-4 K. It takes about 105 seconds to reach this equilibrium temperature, because of the heat capacity of the block.
