Re: What happens to pressure of a balloon placed in a hot room that is open?

If a balloon is moved to a warmer room, it will experience more collisions 
per second on its surface from molecules in the room. Heat is a measure of 
kinetic energy, and the hotter something is, including air, the faster its 
molecules move.  For a short period of time the balloon's volume should 
diminish as its molecules are not pushing out as much as those of the room 
are pushing on it.  After some period of time the molecules in the 
balloon will receive more kinetic energy from the room's molecules (i.e. 
they will heat up) and the balloon will expand slightly.
Whether the room is opened or closed, should make little difference. Air 
in a closed room will eventually have the same temperature everywhere, 
floor to ceiling, but for realistic times the temperature is a little 
different at the ceiling than at the floor, and when the door is opened 
the room will gradually cool off or heat up depending on the outside temp. 
The balloon will change slightly during the time it takes the room to 
change temperature, but not enough to really notice.

Putting a balloon in a hot oven?  The balloon material would probably melt 
before any other thermal equilibrim occurred ( Don't try this at home, it 
would make a mess in the oven and could release toxic fumes!). Put the 
balloon in a freezer and it should expand as the molecules of the balloon 
move faster than air molecules in the freezer. Again the properties of the 
balloon's material will affect what happens, but you would need to look up 
the freezing point of that material to make any more accurate prediction.

You can read more about heat and temperature in "Conceptual Physics" or 
Conceptual Physical Science" by Hewitt et. al. This is a good set of books 
for less mathematical descriptions of topics in physics.