Notice that the equation derived is essentially power times time, giving you the energy loss by heat as H. For simplicity assume the circuit to be DC, the power given is $P={V^2}/R$ or $P={I^2}R$.
Since the transmission line bears huge resistance, according to the first equation using high voltage would means the power is directly proportional to the square of voltage and inversely as the resistance. If we consider the second equation, the power is directly proportional to the square of current and resistance. If the transmission line uses high current, the power converted to heat would be more than the case of using high voltage.