Heat given off by a circuit is a form of energy transfer. In a circuit, the energy of flowing electrons is being converted into thermal energy. This transfer of energy occurs over a period of time and can be described by a rate of energy transfer. Physicists refer to "power" as the rate of energy transfer over time. Now the equation for power of a circuit is:
P = R*I².
That is, the power (P) is equal to the resistance (R) of a circuit time the current (I) squared. This is exactly as you have stated, the heat is directly proportional to the resistance and the square of the current.

So the question is, what happens if we decrease the resistance? Resistance and current are related by "Ohm's law",
V = I*R,
that is the voltage potential (V) across a circuit is equal to the current (I) flowing through a circuit times the resistance (R) of the circuit. So if we have a circuit with a constant potential and we decrease the resistance by a factor of 1/2, then the current flowing through it will double. If we try plugging this into the power equation, we'll see that the power of the new reduced resistance circuit increases by a factor of 2 we shown below:

P=(1/2)*R*(2*I)²
P = (1/2)*R*4*I²
P = 2*R*I²

Because the current term is squared in the power equation, the heat given off by the circuit is more highly dependent on the current flowing through it than the resistance. The heat given off by the new reduced resistance circuit increases.

I hope this answers your question.