Will putting a fan behind a heater lower it’s heat output? I have a small metal coil electric heater and I put a fan behind it to distribute the heat. As far as I can figure, if I cool off the heating elements then I lower the resistance. Will this lower the wattage output of the heater?
 A: Metal resistive coils in the space heaters (and other heater appliances like water heaters) are made of alloys that have more or less constant resistance over their full operating temperature range.
That's why one generally doesn't get measurable increase in the heat output by cooling them.
The total heat output will be increased with the amount of energy the additional fan uses (like, 5-10% in your case on the photo).
The total heat comfort may be quite a bit decreased by the wind created because of the evaporative cooling the human bodies will suffer of (that's why we use these fans in the summer) and the increased heat exchange between the air in the room and the walls. The walls are presumably colder or you will probably not be using a heater in the first place.
On the other hand, your heating appliance may have a thermostat and it may be set to less than the maximum. In this case, an external fan may be cooling the thermostat enough to prolong the periods when the heater element is powered and shorten the period when the heater element is not powered. This may be particularily visible if the air passage of the heater is partially blocked and the thermostat "feels" the heat from the heating coils directly.
p.s.
There are another type of space heaters that use ceramic PTC resistors. They rapidly decrease their consumed power when the heating element heats above some temperature. This is usually considered only a safety feature and these devices are designed to operate well below their self-limiting temperature. The extra cooling will not help. They are usually smaller, quieter and somewhat more expensive, but otherwise the same.
p.s.2
Air conditioning units, when used for heating, can be a great deal more efficient (like, 20-40% more) when their internal heat exchanger is cooled better. They usually have an internal regulator of the fan that can be set to higher or lower speed.
Increased air flow from the AC can have negative impact on the comfort as well. That's why most of them use the "turbo" mode only to reach the desired temperature after they are switched on and then decrease the flow.
A: If your fan cools the electric coils, their resistance will go down and the current flowing through them will go up, and so will the wattage output of the heater.
By the way, the fan inside the heater housing is the primary thing moving the heat off the coils. The fan you set up behind it is mostly moving that heat to distant parts of the room in which it is sitting- which is a good thing.
A: Power = $I^2 R$ and $V = IR$ so power = $V^2 / R$. A simple device like this probably works at constant $V$ rather than constant $I$, so the power goes up when the resistance goes down. The net result is therefore more generation of heat per unit time. If that is what you want then you have achieved it (and your electricity bill will furnish the cost).
A: At least in the US, devices that are designed to by continuously used are allowed to use only 1500 W cite. So most space heaters are designed to use 1500 W. Assuming that the manufacturers design the heaters to compensate for different resistance, they will remain at 1500 W regardless of the temperature of the coils.
