Sudden death?

Hello, I recently got another rescue parakeet. Soon I'll get her cage mate as they're bonded and after explaining why they couldn't separate them, I'll get him today. Anyway, Her former owner had another parakeet that I got first. (It's been a long running negotiation to rescue these birds from their previous elderly owner.) Ive seen it regularly (neighbors) before I got it and took it to the vet. It was slightly malurished but otherwise perfectly fine. I had it for about a few weeks to a month, got it able to willingly be held, slowly gaining weight..or seemed to be at least and, I kid you not, one day it was flying around happy as could be and the next morning it was dead at the bottom of the cage. I do know we had an unexpected temp drop that night, but it wasn't too drastic and I had the cages covered and all other birds are fine. I'm thinking either the temp drop and weight issues were the cause or maybe something else it already had going on that the vet missed. I do know the previous owner had a mice infestation at the time I got him, but I don't know if they can make birds sick or not.
Any ideas?
Again, all my other birds are fine. Just this one that I just got. No birds will be with that owner anymore by today, when I get the last one. Thanks.