Thanks, but:Yes and No!
Most of the thrust is produced by the fan. In a turbofan, the thrust it produces very much relies on the amount of air that by passes the engine core. Modern engines like the one used by the A320 neo, the Pratt and Whitney PW1000G has a by pass ratio of 10:1. That means, for every 1 part of air that goes through the engine core, 10 parts of air goes through the by pass.
As you can see here, the fan makes most of the engine. The actual core is much thinner and smaller.
How it works is simple. A force of same magnitude can be produced by giving a huge mass of air low acceleration according to Newton. This does not only improve the fuel efficiency, it also reduces the chance of thrust losses during different flight regimes. The air that goes through the combustion is mainly used to run the compressors to keep the engine going. Very little of it actually produces the forward thrust. That is why it is sometimes called as residual thrust.
At optimum conditions core may produce only 15% of the total thrust available.
But as the altitude and the speed increases and the rarified cold air thrust decreases too. Engine core’s contribution to thrust at this instance may be as high as 25%.
Bypass ratio can go as high as 24;1
Engine diameter can go as high as 4 meters, currently at 3.6 meters.
But hot portion being zero is out of question, contrary to what was claimed before.