In summers i.e. now, my room has hot uncomfortable air in night, but outside air is cold 4-5 degrees Celsius colder than inside, my room has windows parallel to wind flow, so though wind flows in night it is parallel to my door. Keeping door open doesn't help either it does not replace warm air fast enough.
My assertion is that, if I keep a table fan near door will it help drive cold air inside? How feasible is this solution? Does fluid dynamics provide solution?
Yes sure. This is same as an exhaust fan and ventilators. It will help in driving cold air in.
A way for air to go in and then another way for the air to go out, accompanied with a fan both places is best, though one fan is better than none. There are even those window fans that are two small fans that can run in opposite directions if only one window is available.
Depends on the wall material. For brick and concrete walls, the volume heat capacity of the walls is by powers of $10$ greater than that of air. To cool down the walls $1 \, \textrm{K}$ by air at $-4 \, \textrm{K}$ lower air from outside, you need a storm of $50 \, \textrm{km}/ \textrm{h}$ through the door for all of the night.
Fans cool the wet skin only. There is no effect of a stream of some $\textrm{m}^{3}/ \textrm{h}$ in a room of say, $15 \textrm{m}^{2}$ with $30 \textrm{m}^{3}$ air in it and some tons of hot walls around it.
For experiments, an infrared thermometer with a laser pointer is a nice gadget.
