Puzzle ZHIR 

Workings

Hint
What must the middle midday temperature be? Remember that the temperatures are in degrees Celsius.

Answer
The midday temperatures were -6, -2, 2, 6, 10 °C.

Each day the midday temperature increased by a steady 4 degrees.

Reasoning
As the temperature rose steadily each day, we know that the middle temperature (Day 3) was 2 degrees (because the average was 2 degrees).

Since Day 3 was 2 degrees, and there were two negative temperatures, we know that the daily increase must have been at least 3 degrees (otherwise Day 2 would not have been negative).

If we check a daily increase of 3 degrees, the sequence would be -4, -1, 2, 5, 8, but this doesn't work as the product is less than 500.

If we check a daily increase of 4 degrees, the sequence would be -6, -2, 2, 6, 10, which does match all of the requirements.

If we check a daily increase of 5 degrees, the sequence would be -8, -3, 2, 7, 12, but this doesn't work as the product is more than 2000.

Any larger increase makes the product even larger, so we can stop checking.

So the only possible answer is -6, -2, 2, 6, 10.