Yes, there is an explanation. The flaw is in your intuition (which I admit is very compelling) that "the value of h should be equal to 0 for any value of ‘alpha’ between 0 and 1 given that the Median value of temperatures for Year 1 is less than the Median value of temperatures for Year 2". Although this seems reasonable, it is not the way hypothesis testing works.
What you are seeing could easily arise with any one-tailed test, and it is much easier to see with a one-tailed Z test, so let's consider that. The null hypothesis (Ho) is that a score comes from a normal distribution with mean 0 and variance 1, and let's say we want to reject this Ho, thereby concluding that the mean is actually larger than 0, only if the observed score is "too big". It would be typical to set alpha=.05, which determines a z-score cutoff of 1.645, because only 5% of the standard normal distribution is above 1.645. So, if we observe an actual score greater than 1.645, we reject Ho and conclude that the mean is larger than 0.
Now suppose we choose a really large alpha instead---for convenience say alpha=.95. That determines a z-score cutoff of -1.645, and we are now in a position of concluding that the mean is greater than zero any time we observe a data value larger than that, which of course includes a lot of data values below the hypothesized mean of 0. This is analogous to the strange reversal you are seeing with the ranksum test.
Remember, one-tailed alpha is defined as the probability of rejecting Ho in a certain direction given that Ho is true. If you let alpha grow large, then there will be a lot of observations where you will reject Ho even though the evidence is quite consistent with it or even points to a reversal of it. That doesn't come up in practice, though, because people always choose alpha to be rather small.
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