Kinda, but not quite. I now have the time to give a proper explanation, though:

Thermodynamic Beta is a measurement of a system, proportional to dS/dE. Conceptually, it tells you how much entropy a system will change by when you add/remove a bit of energy. The best way to understand this is to go back to the basic definition of entropy (handwaving a bit here), where it is defined more-or-less as the number of different possible states a system can inhabit. It's all probabalistic and statistical, frex, a system of 4 coins has a certain number of states (16, assuming the coins are different).

As long as a system can have infinite energy, Beta is always positive, because a system at higher total energy has more possible states it can inhabit. However, in some systems, there is an upper limit to how many possible states there are. For example, taking that coin example, let's say we start with tails, and assume it takes a certain amount of energy to turn a tail into a heads, and that energy is returned when the head turns back to a tail. Say we have 1 unit of energy. Then there are 4 possible states, since that 1 unit of energy can make 1 of 4 coins a heads. 2 units of energy means 6 states. Now, however, when we go further up in energy, we notice something strange: 3 energy leaves us with only 4 possible states, ie, adding energy *decreases* entropy, and 4 energy leaves us with only 1 state, all heads. For any other system where all objects within have a finite number of energy states, the same thing happens, eventually you add enough energy and you decrease the number of possible states.

Then, given the definition of Beta, and consequently the definition of temperature as the reciprocal of beta, you can get negative temperatures in some strange cases.

Root hypothesized that the thermophages may be operating within such a strange system, which might, given the limitations of what he knows when true space magic exists, mean they have a way to neutralize the threat.