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By cooling, the resistance is decreasing, then the current I=U/R is increasing and the total power is increasing also P=U^2/R
R1,2 are the resistance of the 2 halves and R1-r1 and R2+r2, their final resistance, because, due to the first half cooling, R1 is decreasing and R2 is increasing, because the current and temperature are increasing.
We consider that 2(r1-r2)/(R1+R2)<r1/R1, so the heat released in the chilled half is decreasing and in the unchilled half, is increasing.
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