How do these two sentences differ in meaning? Thank you.
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I don't think there is really much difference between the two sentences.
昨日雨が降っていた時に "at the time it was raining".
昨日雨が降っていた時は "As for the time it was raining"
In the second sentence "the time it was raining" is introduced as a topic so it is expcted that the listener already has some knowledge that this event happened.
The は in the second sentence could also be seen as a contrastive marker. i.e I was at home at the time it was raining but I was out for the rest of the time. Either way, I don't think it really changes the meaning in these examples.
Perhaps a native speaker can see more of a change in nuance.