There might be a *big* problem with using only one layer of elements in solid-2.
* On the boundary of 1/2 do they (i) share the same node numbers or, (ii) have separate node numbers, so you tie together the temperature dof using MPCs?
* If (i) above: which INITIAL CONDITION, TYPE=TEMPERATURE is last in the input file? This is the one which will take precedence for the boundary layer of nodes, so if that last IC refers to Solid-1 then you only have the nodes above the boundary in Solid-2 set to 2000K.
* If (ii) above, in which direction is the MPC? The node on Solid-1 should be tied to the node on Solid-2 to ensure the 3000K IC holds; not "2" tied to "1".
* In any case, there is an enormous temperature gradient across the single element height of Solid-2 - hardly the conditions for a stable solution!
* what kind of elements are you using: first or second order?
As Corus states, the thermal capacity of the two solids would appear to be enormously mis-matched, so without further heat added the final temperature of the two will be close to 300K (work it out using the relative heat capacities and volumes/masses).
As Corus suggested in the earlier LENS thread of yours (I've just looked at) to get reasonable results near the interface you need more mesh refinement and certainly more elements height-wise in Solid-2. As he also suggested in that thread, you can take advantage of two vertical planes of symmetry to cut down the model size - or do 2D trial solutions to get a feel for the problem. You'll make far more progress understanding what's going on rather than throwing everything into a large 3D model. You'll see and understand how the thermal transient progresses into the depth of solid.
I also notice in that LENS thread a very surface heat flux of 1e08!!! Presumably that's W/m^2. That's probably the reason for your strange results there. You would need either much smaller time steps or much more mesh refinement to get accurate results in the early and intermediate stages of the transient.
Now I'm not a thermal transient thermal analysis specialist, but I recall there's a recommended size of size step per increment depending on minimum mesh size and thermal conductivity at least. (Corus will know.) You must take account of that in setting your time steps, or refining your mesh.