To find the percent increase in temperature, you can use the following formula:
\[ \text{Percent Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]
In this case, the old value (initial temperature) is 625°F and the new value (final temperature) is 1034°F.
First, calculate the difference:
\[ \text{New Value} - \text{Old Value} = 1034°F - 625°F = 409°F \]
Now, plug the values into the formula:
\[ \text{Percent Increase} = \left( \frac{409°F}{625°F} \right) \times 100 \]
Calculate the fraction:
\[ \frac{409}{625} \approx 0.6544 \]
Now multiply by 100 to find the percent:
\[ 0.6544 \times 100 \approx 65.44 \]
Thus, the percent increase in the temperature of the liquid is:
\[ \boxed{65.44} \]