1. **State the problem:** The temperature was initially $-16$ degrees and it rose by $23$ degrees. We need to find the new temperature. 2. **Formula and concept:** When a temperature rises, we add the increase to the original temperature. So, the new temperature $T_{new}$ is given by: $$T_{new} = T_{initial} + \text{rise}$$ 3. **Substitute the values:** $$T_{new} = -16 + 23$$ 4. **Calculate the sum:** $$-16 + 23 = 7$$ 5. **Interpretation:** The new temperature is $7$ degrees. **Final answer:** The integer describing the new temperature is $7$.