Is heat transferred in our atmosphere by conduction?
Did you mean into our atmosphere from space or within it?
A very small amount of conduction may occur within the atmosphere. Practically speaking there is no net heat transfer into the atmosphere from space.
Gases have very low thermal conductivity values because their molecules have very little effect on each other, i.e. in order to transfer kinetic energy from one to another. Those values will decrease further the larger the altitude as the density of the gases will decrease. Therefore, heat transfer within the atmosphere by conduction is very small. Convection is the dominant heat transfer method within the atmosphere: think wind!
As for heat transfer from space into the atmosphere the predominant method is by radiation, and that from the Sun. Space is a vacuum and so there is no matter to sustain either conduction or convection. Electromagnetic waves, however, can propagate through a vacuum so infrared rays emitted by the sun can travel through space to the Earth,