I would like to increase candle flame emission without messing up it’s brightness/contrast.
I would like that the candle flame would light up the whole room but would keep it’s current brightness/contrast, because when I just increase emission enough to light up the whole room the flame becomes white.
As Alfred Hitchcock famously said to Ingrid Bergman: “Ingrid, fake it!” :yes:
Your candle does not … actually … have to “light up that room!”
Instead, it must merely “plausibly appear” to do so.
Important difference.
There will be many sources of light in the scene to provide, first, “basic overall illumination,” then, so-called “practical lights” including your candle. The practical lights are not counted-on to provide any actual illumination in the scene, yet the light sources which do provide this illumination are planned to support the viewer’s pre-conceived notion that the candle is providing the light.
A candle in real life does not emit that powerful of a light, the only area with decent illumination would be the area around it.
To really light a room, you need lots of candles (but Cycles cannot do that easily unless you change your tonemap settings to something more realistic, as the default settings will quickly burn out your light sources when raising the power)
“Nawww, forget the ‘lots of candles.’” 
Speaking in BI terms, you’d first need a shadowless “sun lamp” – or even “global illumination” – to provide an even, shadowless, slightly-cool “basic exposure” to the entire scene. Then, perhaps a nice soft-edged spotlight overhead to provide “the glow of the candle.” Then, if the candle needs to particularly expose specific things in the scene (because the camera is looking at them), separately light those things. If you like, animate the intensity and/or the color of a few lamps in a few shots.
Now … shadows? How about my old best-friend, the “shadow-only spotlight!”
“The candle, itself,” is a so-called practical light: the viewer recognizes it as a light-source in the real world, but in your actual lighting setup it probably doesn’t do anything. (Because it is puny, and because that would just be too hard to light.) In the BI world, sources of light are never visible even when the camera is looking right at them, so you can stick a lamp inside your candle – just like Sir Alfred once famously put a light bulb in a glass of milk (that turned out to just contain … “milk”).
Measure both the spread of light vs. dark in the scene, and the spread of color tones. Establish a standard for the scene so that each shot, no matter how it is (individually …) set up, will produce a final result that is comparable with all of the others. You can do this acceptably well for planning and set-up purposes with OpenGL Preview renders, followed by a few selective “real” ones of individual frames to confirm your results.
But: "how the light appears to be, to the audience, really has little or nothing to do with what is needed, in the cinematography design, to support the needs of individual shots.
Expect to make heavy use of compositing to assemble(!) the final frame. None of your individual renders – which produce components of the final masterpiece – will closely resemble that masterpiece. It is during the compositing step that you make everything come together.
Also carefully consider that you can combine Cycles outputs with BI and even with OpenGL, leveraging each rendering technology at the same time to best suit the needs of each shot. Yes, it takes a good bit more planning, but it’s worth the trouble. (You’d be amazed at what OpenGL technology can do these days!)
If you simply try to do it with “one Cycles render after another,” each time trying to “imitate the real world,” you’ll never have a product to deliver. :no: CG is not the real world. CG is an artful contrivance. A fake. But, a really good fake.
If you are rendering is Cycles - use this node setup.
This allows separate control of the emitted light that lights up the room - and the emission if the flame itself.
Using this trick allows you to project more light into the scene - but avoid making the candle flame itself too bright (have made the two emission shaders different colours for the sake of clarity - so you can see the effect).
… and, while duly acknowledging the technical virtues of that comment … “the candle does not actually have to light up the room!”
In every stage play, the room is filled with lights. When the actor walks out on stage holding a candle, you know perfectly well that the candle is not lighting the theater. (You could not bear to look at it, if it was!) However, the stage lighting changes subtly to mimic the close lighting that suggests that the candle is the primary source of illumination. However, you also notice that “the stage is not dark.”
It is for this reason that (IMHO) “it is an enormous waste of time” to try to “imitate reality,” even though of course you can do so with CG.
“You are here to put on a show,” shot by shot by shot. Everything about each shot – camera angle, focus, lighting – must seamlessly support the aims of the picture. And, each one must be sufficiently consistent with the others that the viewer, upon watching the completed film, does not “detect the trick.” (The shots can actually be quite inconsistent with each other, so long as the viewer does not “stop ‘suspending his disbelief.’” For instance, Star Wars® Episode One shipped to theaters with a “pod-racer crowd” that consisted of variously-colored Q-Tips® cotton swabs! No one noticed, because they had seen an “actual crowd” moments before. So it goes.)
Our brains are wired to see what they expect to see. (Recall the “PARIS IN THE [THE] SPRING” pyramid.) Use this to your advantage. They really have no idea how the trick was done, as long as it matches their expectations of, in this case, “a candle-lit scene.” (Neither do they care: they’re too busy munching popcorn and necking in the back row.) 
Although I fully agree with everyone and your points, in this particular case (to achieve the desired effect) I’d either do moony’s approach on separating the shaders (or what goes into them), or simply add a point light above the flame. The flame itself I might set to camera visible only.
I’m pretty sure a stage lighter or photographer would have used different tricks if they had access to invisible lights.
Except for the fact that not everyone is doing CG in order to imitate live theater or physical filming setups (and shouldn’t be seen as literally the only way to break reality if needed). You have tools and features like lightpaths so you don’t have to model softboxes, gobos, and spotlights for your lighting setup, you don’t have to model an environment that literally look like set pieces placed on a stage (though you can if that’s how you want to work for some bizarre reason).
As long as it looks good, then there’s no right or wrong way to do things really (but don’t be telling people that your idea of faking everything is literally the only valid way to work in CG).
try a light falloff node set to linear. constant if you really want to shine
it plugs into the strength.
EDIT: i guess we dont know your setup. the above will only work with lamp objects, which are faster then mesh lights IMHO.