See Eli’s post.
Eli can keep on adding plates, Ms. Rabett has gone out to buy some extras. Here is the red plate special. If somebunny works it through they will find that b’=3/4 a, go another plate and, as Christian pointed out, now b’ has increased to 4/5 a and so on.
Eli has not said anything about how the heat is being transferred, radiation, convection or conduction but since heat transfer, no matter the mechanism, is always proportional to temperature, the temperature of the blue plate must increase as more plates are added.