If specific heat of a substance is infinite, it means
No change in temperature takes place whether heat is taken in or given out
Specific heat capacity is the amount of energy required by a unit mass of a substance to change its temperature by 1∘C or 1∘K.
If specific heat is infinite, than it takes an infinite amount of energy to change its temperature even by 1∘C . Thus, no change in temperature takes place even if you add or subtract heat.
Q=m.c.△θ
c=Qm.Δθ
If Δθ=0⇒c=∞