How do I correctly place "the" in the following sentence?

I'd keep the first sentence. "The" is a definite article, you should use that to emphasize a certain noun in the sentence and make it "unique" so to say. Over-using it will take its emphasizing power away.

Breakdown of your sentence:

"The analysis shows that the most important parameter..." - the "the" is there to emphasize this specific parameter over the others

"...affecting conductor temperature..." - in infer from context that we're talking about an already predefined conductor or about conductors in general, so there is no need to make a distinction between one specific conductor over others, or one specific conductor temperature over others

"and hence power was the ambient temperature" - again I'm inferring from context that you're talking about either a predefined power or a generic power. In this part I'd also remove the "the" preceding "ambient temperature" as I don't see value in making this stand out from the rest of the sentence.

The second sentence reads a little bit like it was written first in a Latin language and then translated due to the extensive use of definite articles preceding the direct objects.