You've told us only that the temperature varies linearly with altitude.
That's very nice information, but you haven't given us the slope of
the linear variation, or any initial point. There's no way to answer
the question without those numbers.
It's really too bad about the delicate instruments failing and all that.
But it sounds like they were working OK at some time before they
failed, so you must have received at least one good temperature
reading. Tell us what that one was, and maybe we can work toward
an answer.
