> Is there an explanation for this result, or is it wrong.
The result looks correct. The Fourier transform shows a large DC component, because the signal has a large DC component.
> I'm new to digital signal processing, so I'm a bit confused: shouldn't DC gain be negligible?
What do you mean by "DC gain"? From the graph, it looks like the average value (-> DC component) is about 32.75°C, and all other variations are in the +/- 2.5°C range. A large DC component in the frequency domain correctly represents the temperature data.