An Equilibrium Problem

Just posting a problem here (and assorted random thoughts potentially related to the problem) so I won't forget it later. Reader input (e.g. "You are an idiot for being stuck on this problem!") is welcome, too.

Story:
At work, it is routine to measure the pH of a sample. However, the pH meters are all calibrated to accept samples at 25 ^oC, while the samples themselves can be at various temperatures; rarely are they exactly at 25 ^oC.
Now, we have a water bath (set to 25^oC) for storing buffers, so some people put the sample in the bath and wait until it reaches 25 ^oC before measuring its pH, checking with a thermometer occasionally. On the other hand, other people just take the pH of the sample directly, claiming that the difference in pH due to temperature is negligible and that waiting for so long before taking the pH is a waste of time. As my supervisor happens to be of the latter persuasion, I am pretty much obligated to take the pH of the sample directly. However...how off will my value be from the true pH value, assuming that my pH meter is perfectly accurate?

Problem:
Suppose the pH of a solution is 11.60 at 25 ^oC. What is the pH of the solution at say, 30 ^oC?

Obviously, there isn't enough information to solve the problem. So, let's say we are given a CRC handbook, and a second-year thermodynamics textbook. But using thermodynamics equations leads to new problems, e.g. do we use the linear or polynomial approximation(s)?

Also - do we need to know all the relevant species and their concentrations in the system? In real life, the solution is some complicated mixture containing many species, including amines with lots of functional groups, dyes of unknown constitution, sodium carbonate, hydrated transition metal cations, sodium sulfite, and so on. Of course, I can simplify matters and claim that the mixture is simply a carbonate-bicarbonate buffer, with equal concentrations of each species before dissociation (say, 0.18 M). But that'd be cheating.

Of course, the easiest way out is to just measure the solution's pH at two temperatures. But that isn't nearly as fun. More to the point, in real life the pH meter has a tendency to drift, so the result is definitely not perfectly accurate.

Something to think about at work, I guess...along with some other stuff. Like trying to avoid being toasted at work for not noticing certain trends (yep, got toasted this morning, kind of like failing a pop-midterm. That wasn't fun.). One thing is certain, though: we never see interesting tidbits like this on a first-year chemistry final. Sad, isn't it?