This is not a direct answer to your question as I am not sure whether the instrument you described exists, but OP would probably find the mathematics behind transmission congestion contracts very interesting.
Transmission congestion contracts enable the hedging of fluctuations in electricity prices across the power grid, and are auctioned off by regional utilities operators. When demand for electricity in a certain area outstrips the immediate supply, electricity prices and operator expenses increase as the grid transmits power from more distant locations. These contracts derive their value from the demand for power at any one of thousands of transmission points (power stations).
They are not basket derivatives and there is no direct relation to weather in the pricing formulae, but as you could probably guess there is a strong correlation with weather in the value of these contracts.
General pricing inefficiencies, heat waves, blizzards, outages etc. can all make for highly profitable arbitrage opportunities. Trading firms large and small have successfully entered these markets in the past 10 years, arguably to the detriment of the power operators these contracts were designed to benefit.