"I heard (that) it will rain tomorrow" In this sentence I know we should use will However "I thought she will/would go there tomorrow" Why should we use would and not will in this sentence? What is the difference between the two sentences?
The difference is the first example sentence uses the verb "heard", but the second uses the verb "thought".
Saying you "heard" something in the past implies that it's what you believe in the present, so whatever you heard about the future can be stated with normal future grammar. On the other hand, saying you "thought" something in the past means it's your past belief, so you have to state that belief in the past tense.
To compare more clearly, let's only switch the first verbs in your example sentences:
"I thought it would rain" and "I heard she is going there tomorrow" are both correct.
"I thought that she will go there tomorrow" is never correct.