Select the most appropriate idiomatic expression that can substitute the underlined segment in the given sentence.
He is very strict with his students but good-natured.

The correct answer is "his heart is in the right place".

Let's analyze the given sentence and the idiomatic options to understand why this is the most appropriate substitution:
The sentence reads: "He is very strict with his students but good-natured."
The conjunction "but" indicates a contrast. While he displays a strict demeanor on the outside, his underlying nature, intention, or character is kind, caring, and well-meaning (good-natured).

Now, let's look at the meaning of the options provided:
1. "his heart is in the right place": This idiom is used to describe someone who is fundamentally kind, well-intentioned, and good-natured, even if their outer behavior, appearance, or actions sometimes seem harsh, strict, or clumsy. This perfectly matches the context of being "strict... but good-natured".
2. "his eyes are bigger than his stomach": This means someone has taken more food than they can actually eat. This is unrelated to being good-natured.
3. "he has a big mouth": This describes someone who talks too much or cannot keep secrets. This does not fit the context.
4. "his heart misses a beat": This expression is used to describe a feeling of sudden excitement, fear, or surprise. It does not describe a person's character or temperament.

Therefore, the idiom "his heart is in the right place" is the most suitable substitute for good-natured in this sentence.