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A dict.cn example sentence for 热烈 is:
他因受到热烈欢迎而高兴
tā yīn shòudào rèliè huānyíng ér gāoxìng
He was pleased by the warmth of his welcome.
The translation is mostly straightforward:
But I don't understand what these two are doing in the sentence:
Question: What are 因 and 而 doing in the sentence 他因受到热烈欢迎而高兴?
I would probably phrase it like 他很高兴因为他受到热烈的欢迎.
[因 A 而 B] = [because of A, therefore B]
[因 A (受到热烈欢迎) 而 B (高兴)]
[Because of A (受到热烈欢迎), Therefore B (高兴)]
or
[B because of A] ; [B for A]
[B (高兴) because of A (受到热烈欢迎)]
[B (高兴) for A (受到热烈欢迎)]
When A is a reason; B is an action
When A is a cause; B is a result
Your interpretation "他很高兴因为他受到热烈的欢迎. " is correct.
As I posted in the comment above, the "because...so..." structure is wrong in English, so we have to use one word ("because", "as", "for" and etc.) to interpret here.
"因 A 而 B" could be translated to "B as(or for) the reason A".
Compare with "because" and "as", I opt for "as" because "as" usually expresses the more casual reasoning than "because".
The translation for the whole sentence might be:
He is happy as he is warmly welcomed.
"因 ... 而 ..." is just another way to say "because". They come together.
他很高兴因为他受到热烈的欢迎.this stress his is happy.
他因受到热烈欢迎而高兴 this stress the reason maked he happy.
