Distillation of methanol and water - Temperature Change
The thermometer that records the temperature is in the air high above the solution (usually above a Vigreux column). Your distillation was under ambient conditions, so there was air in contact with everything.

The thermometer can only records a rising temperature if the temperature around it rises. During the distillation, this is due to methanol vapour (around $\pu{70 °C}$) which can also condense on the thermometer to transfer heat.

Once all methanol has been distilled away, there is nothing coming from below that could transfer any additional heat: water, sulphuric acid and benzoic acid all have far too high boiling points and low vapour pressures. Thus, the thermometer is again in contact with the surrounding air and cools down.

While I have described this with air, basically the same thing will happen in a vacuum distillation, too.