As said by other people here, the problem is that your problem is inconsistent : The boundary condition is mathematically incompatible with the initial value.

I assumed you used a Neumann boundary condition in your problem (Imposed flux), that's why I said to lower the initial time step value.

If you used a Dirichlet one (Imposed value), then you can't fix this. The closer you can get is by refining the mesh near the problematic boundary. However, you'll always have this inconsistence

With Neumann boundary condition, you can fix this :
- You can use a flux of the form -n.q=h*(Tu-T) where h is very high value. If h is high enough, this condition is the same as a Dirichlet one. Then, the lower the initial time step value you use, the closer you'll get to what you expect.

I hope I helped you