Stella said that she's found a way to take Amy's temperature that seems to cause her much less discomfort, which is good to know. This morning, it was 37.8 °C (100.0 °F), so there seems to be no more cause for concern. She also didn't take a nap at noon, even though she was in her pushchair, which is a good sign.
Stella told me this evening that she thought that Amy was ill comparatively often this winter, with the sniffles or throwing up or this or that, and that she had found that unusual since Amy was very rarely ill before.
After she gave the matter a bit more thought, she remembered that last winter, she had still nursed Amy, partly because she had read that it's better not to wean a child just before the winter. (She ended up nursing Amy for 2y7m—a month later than planned since Amy had fallen ill.) So this winter was the first that Amy had to master with her immune system left to its own devices.
Correlation doesn't equal causation, but I can well imagine that it was a factor.