Yes, a QST is subjective in the sense that you rate the pain you feel (or don't feel) via numbers of 0 to 100. But it's also objective in some parts. A QST is standardized.
First, your perception of cold and hot and your ability to distinguish warm from cold is tested. For this, a machine through which water gets pumped with a plate is put on the hand and then foot. Then the plate gets warm (up to 50°) and cold (down to 5°) very fast. This is objective in the sense that the tester knows when the plate is warm or cold, and if you say "cold" when it's actually warm it shows - if you don't cheat - that you have a problem.
Then you have to say at which point of warm or cold you feel pain. It's normal to feel too low or high temperatures as pain. This is subjective in a way. There are normal ranges.
For me, at 50° I started to feel pain, and 5° weren't painful at all.
The test goes on with little "needles" which are punched with a standardized force into the hand and foot. (For me, this was absolutely not painful.) Regarding pain, the rating is subjective. You have to distinguish during this test if a needle is pointed or flat. This, again, is objective.
In the last part of the test it's about pain rating alone. Objects like a q-tip, brush, needles are put on the hand and foot in a certain order and you have to say how painful that is for you. Here's also the "repeated punch leads to pain test". For me, this was barely/not painful and some needles I couldn't feel at all.