This example illustrates the basic concept of conduction heat transfer through a plane wall.
T(x) = T1 - (T1 - T2) * (x/L)
Assuming A = 1 m², T1 = 100°C, and T2 = 0°C:
q = k * A * (T1 - T2) / L
q = -k * A * (dT/dx)
Here's a piece related to heat transfer, specifically on the topic of conduction heat transfer: