1. We need the element that remains liquid inside pure boiling water.

2. Pure boiling water is at approximately $100^\circ\text{C}$ (at 1 atm).

3. For a substance to remain liquid at $100^\circ\text{C}$, its melting point must be below $100^\circ\text{C}$ and its boiling point must be above $100^\circ\text{C}$.

4. Check each option:

   A: Li (Lithium)

   • Melting point $\approx 180.5^\circ\text{C}$
   • Since $100^\circ\text{C} < 180.5^\circ\text{C}$, lithium is still solid.
   • So, not liquid.

   B: Br (Bromine)

   • Melting point $\approx -7.2^\circ\text{C}$
   • Boiling point $\approx 58.8^\circ\text{C}$
   • Since $100^\circ\text{C} > 58.8^\circ\text{C}$, bromine would be gas/vapour, not liquid.
   • So, not liquid.

   C: Cs (Caesium)

   • Melting point $\approx 28.5^\circ\text{C}$
   • Boiling point $\approx 671^\circ\text{C}$
   • Thus at $100^\circ\text{C}$, cesium is liquid.

   D: Ga (Gallium)

   • Melting point $\approx 29.8^\circ\text{C}$
   • Boiling point $\approx 2204^\circ\text{C}$
   • Thus at $100^\circ\text{C}$, gallium is also liquid.

5. Now note the important practical chemistry point: inside pure boiling water, the element should remain liquid without reacting with water.

   • Cs reacts violently with water, so it will not simply remain as a liquid metal in boiling water.
   • Ga does not react with water under these conditions and can remain as a liquid.

6. Therefore, the correct choice is:

$\boxed{\text{D: Ga}}$