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Yes, temps are a factor, because engine intake temps will increase in warmer months. This means higher chance for detonation.
Assuming you have a 12 gallon tank, your fuel's octane rating on your change-over tank would have been approx:
2 x 93 = 186
10 x 87 = 870
870+186 = 1056
1056/12 = 88
So you'd have had 12 gallons of 88 octane fuel, approximately. Simple averaging is all you need to determine a mix of octane ratings.
Yes, it is possible that the ECU had to experience a re-learn with the new fuel. Being OBD-II compliant kind of makes it difficult to speculate without actually knowing how the ECU compensates for potential knock (detonation).
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