Heat produced by the heater will be same. When the bulb and a heater are connected in parallel and this combination is connected across the mains, potential difference across each is the same equal to the voltage V of the mains irrespective of the resistance of the bulb.
If R is the resistance of the heater then heat produced by the heater will be \(\frac{V^2}{R}\) in both cases. Hence heat produces by heater will not be changed.