Will a CFL light bulb and an incandescent light bulb produce exactly the same amount of overall temperature increase over time? Will a CFL light bulb and an incandescent light bulb, in separate respective closed systems, produce exactly the same amount of overall temperature increase over time?
Assume you have two identical closed systems with gray walls, with a system input of 20 watts of power each. 
EDIT added for clarity: (On the packaging of the CFL light bulb the large print equivalent wattage is irrelevant... the input current of both bulbs is a consistent 20 watts of power each.  The comparison wattage vs. the actual wattage of the CFL is off subject.)
One has a CFL, one has an ordinary incandescent light bulb. Will both systems increase in heat the exact amount, every hour?
Due to conservation of energy it shouldn't matter if one light source is more efficient, right?... it's the same amount of energy input. One light makes more heat one makes more light, but the light when it hits the gray wall is converted to heat, right?
There is no such thing as loss of energy... it's just converted to another form of energy... and light is converted to heat, right?
The back story of this question is my wondering that if my wife leaves an incandescent light bulb on in the winter time it's not so bad because even though no one is in the room it's still heating up the room.  On the other hand if she leaves on a CFL it's more efficient but it should still add heat to our "system," i.e., our home.
 A: No they won't
if you're reading the "watts" off the package.
That is because for an incandescent bulb, the "60 W" is a measure of the actual electric power it dissipates.  Most of that power is thermal (i.e. heat) from the get go, and every last Watt ends up heating in the room eventually (when the light energy thermalizes).
On the other hand, CF lamps and LED lamps are labeled with "light output equivalent" wattage, because the first thing people care about when buying a bulb is how much light they're going to get and we've grown used understanding that in terms of an incandescent bulb's total power dissipation (I suppose that in twenty years this will look like a really stupid convention to the kids). If you read the package closely you'll see that high efficiency lamps generate about the same amount of light, but much less heat. The relationship is not linear in equivalent wattage, but runs about 1/7 for CF bulbs in the 60--120 "Watt" range.

Yes they will
if you really mean, that each bulb dissipates 20 Watts.
However, that's a really dim incandescent bulb suitable for little more than a night light, but a pretty good CF bulb suitable for keeping a medium sized room well lit and allowing you to read comfortably.
A: The relevant comparison is between bulbs with similar light power.
Let's assume for sake of argument that a 20 W CFL light generates as much light as a 100 W incandescent bulb. For instance, both generate 5 W of light. If you leave the CFL light burning in a room, you get 15 W of heat and 5 W of light. If the room has no windows, no light energy leaves the room, and the room heats up with a rate of 15 + 5 = 20 W. In the same room, the incandescent light gives 95 W of heat plus 5 W of light, for a total of 100 W of heating power.
It is generally not a good idea to heat up your home with incandescent bulbs (or any other form of electrical heating) as it takes much more energy in the form of hydrocarbons to generate a given amount of electrical energy. Efficiency wise, is better to heat up your home by burning the hydrocarbons locally.
And where the difference between CFL and incandescent bulbs really starts to matter is during summer when each Watt of power dissipated in your home needs to get pumped to a hot outdoor environment using an AC.
A: The answer is yes, of course both will produce the same amount of heat energy.  Any electrical load with an input of 20 real watts will output 20 watts, in some form or other. In a perfectly insulated box, all of that energy will eventually be converted into heat because no energy conversion is 100% efficient.
Doesn't matter if the load is an incandescent bulb, a fluorescent bulb, a motorized egg whisk, or an air conditioner.  If it uses 20 W, it will eventually produce 20 W of heat.
Reactive power is a different story, since the energy is temporarily stored in the load and then returned to the power line.
As for the rate of temperature increase, I'm not sure, since the ratio of different forms of energy in in the box will be different, even though the total amount of energy in the box will be the same.  Does light count towards temperature?  Temperature is a measure of the kinetic energy of particles.  Does a perfectly mirrored box with light bouncing around but no particles inside have a temperature?
A: no they will not
because cfl bulbs consumes less energy
