@abcd thanks for you comprehensive study. I looked at your steps and I like your approach. To help you move forward on this I think you can specify both the mesh size and time step in the solution like this

pds := pdsolve(PDE, IBC, numeric, time = t, range = 0 .. L1+L2, timestep = 1/10, spacestep = 1/10)

Hopefully changing dT and dx would help. I look forward to hearing your findings on this.

Thanks @marc sancandi your suggestion got rid of the error. But it's giving me non-physsical answer. This problem is a transient heat problem with one side being exposed to hot air and the other side being exposed to cold air. I'm expecting to see a smooth change in temperature change in the wall but the results don't look physical. Any suggestion?

>T01 := 278; T02 := 26; L1 := .1; L2 := .2; h1 := 10; h2 := 10; k_cnc := .8; k_soil := 2.45; rho_cnc := 2500; rho_soil := 2100; cp_cnc := 750; cp_soil := 1459; alpha1 := k_cnc/(rho_cnc*cp_cnc); alpha2 := k_soil/(rho_soil*cp_soil);
>PDE := {diff(T(x, t), t) = alpha*(diff(T(x, t), x, x))};
>alpha := piecewise(x < L1, alpha1, alpha2);
>IBC := {T(x, 0) = T02, (D[1](T))(0, t) = h1*(T(0, t)-T01)/k_cnc, (D[1](T))(L1+L2, t) = -h2*(T(L1+L2,t)-T02)/k_soil};
>pds := pdsolve(PDE, IBC, numeric, time = t, range = 0 .. L1+L2);
>p1 := pds:-plot(t = 0.1e-2, numpoints = 200); plots[display](p1);