Step 1: Examine each kingdom with respect to cell wall and mode of nutrition.
Plantae: Have cell walls (cellulose) but are autotrophic (photosynthetic).
Fungi: Have cell walls (mainly chitin) and are entirely heterotrophic.
Animalia: Are heterotrophic but do not have cell walls.
Protista: May or may not have cell walls, and can be autotrophic or heterotrophic.
Step 2: Identify the kingdom satisfying both conditions.
Only Fungi possess:
a definite cell wall, and
exclusively heterotrophic mode of nutrition.
Hence, the correct answer is
\[
\boxed{\text{Fungi}}
\]