Did a distillation between two solvents. Would the answer have to do with temperature?
There is no such point when the first solvent is completely distilled and then the next one starts. From the very beginning, both solvents boil together, though the vapor initially is relatively enriched with the lower-boiling one. The cutoff point is set somewhat arbitrarily. And yes, the answer surely has something to do with temperature, because temperature is the only parameter we can control.
Like NotNicolaou said, if the boiling points of your solvents are reasonably far away, you may separate the mixture almost completely by collecting the fraction that distills near the boiling point of the low-boiling one. Otherwise, you might not be able to get pure compounds, unless you use an industrial rectification column.
The answer would depend upon how different the boiling points of the two solvents were.
If the boiling points were completely different, say one component boiling at 40 °C and the other at 250 °C, then heating the mixture to 40 °C would remove all of the component boiling at that temperature, leaving the 250 °C boiling component behind. This the principle of a rotary evaporator, with the high boiling component often being the product of a chemical reaction.
If the boiling points are similar, say 70 °C and 80 °C, then it can be harder to get complete separation. Often in these cases, three 'fractions' are obtained: clean 70 °C material, clean 80 °C material, and a small amount of a mixture which distills off between the two. In this case, a fractionating column (such as a vigreux column) can be used, to get better separation. The boiling point of the distillate can always be measured, as an internal thermometer is often used and as such its possible to see whether the boiling point of the distillate is cleanly 70 °C, cleanly 80 °C or some in-between number (indicating a mixture is being distilled).
Its also worth noting that many solvents form azeotropes with water, and in these cases (such as benzene and water) it is not possible to cleanly distill the two components apart despite the different boiling points, since the mixture has a defined boiling point which is neither that of benzene nor that of water.