Fire a neutrino from whatever starting point and in whatever direction you like in the universe. As the neutrino travels, it will traverse many temperature gradients in its ambient environment. What path should you choose to maximize the number of reversals of temperature gradient encountered along the path? Equivalently, the goal is to maximize the number of temperature maxima / minima encountered along the path. Of course, I'm interested in getting some estimate of how many gradient reversals are attained as well.
For example, say I fire the neutrino downward from inside my refrigerator at midnight. Then the temperature increases upon leaving the refrigerator, decreases upon leaving the house, increases and then decreases as it passes through the earth, increases briefly (I think?) on its way through the atmosphere before decreasing again, then increases and decreases again on its way through the sun, etc. We're counting the number of times we switch between increasing and decreasing.
Temperature is hard to pin down precisely, so let's stipulate that we always average the temperature over the ball around the neutrino of minimal diameter such that the expected number of particles within the ball is one mole, and we only count a temperature gradient reversal if the average temperature has changed by at least 1% in absolute terms.
I think that should make the question reasonably well-posed, but perhaps there's something I'm neglecting. Also, this is a kind of weird question (and I'm not an experienced physics SE user) -- I'd appreciate any help in choosing appropriate tags.