Do you know the word to describe a cool rushing current of uphill air? I think it has something to do with the air coming from a cool place on a warm day.
This can be called a thermal.
In the context in which you asked it's very similar to updraught but there are ways that the words could be used differently.
Regarding @RegDwight's comment, these are caused by a body of air becoming heated and rising; cooler air will be drawn into the vacuum created when this happens. If this occurs on a hill it can cause cool air to be drawn uphill.
The spelling updraught has been used here instead of updraft as the question has the British-English tag.
I believe you're looking for Updraft. This fits almost exactly what you're describing and can be used for both indoor and outdoor settings.
"Do you feel this updraft?"
"Yes. Let me close the window."
Note: Niall's answer gives the British-English form, updraught, which is likely a more correct word that you were after. It's worth mentioning that they both are identical in meaning.
The wikibooks High School Earth Science/Air Movement document, in its Mountain and Valley Breezes section, refers to cooling breezes that move uphill as valley breezes. Also see wikipedia's Mountain breeze and valley breeze article. Note, in the Land and Sea Breezes section, similar cooling breezes moving onshore and uphill are called sea breezes.
Generally, a warm wind moving uphill is called anabatic, and a downhill wind, typically but not always warm, is katabatic wind. (Typically, adiabatic warming occurs as a parcel of air descends and compresses, and adiabatic cooling as it ascends.) Many of the 85 to 100 or so individually-named winds listed on wikipedia's Category:Winds and List of local winds pages (such as Chinook, Föhn, Santa Ana, and Zonda winds) are katabatic and hot. Some cool winds are the tramontane, Cierzo, mistral, and Piteraq. Valley exit jets typically are cool downhill winds. Orographic lift refers to air cooling and drying as it is forced up a mountain slope. (Also see Orographic Lifting and Rain Shadows at waterencyclopedia.com and Some Basics of Mountain Flow at blogspot.com.)
Summary: Relevant terms include valley breeze, sea breeze, anabatic, valley exit jets, and orographic lift.