:does increasing temperature increase pressure? which type of investigation would most likely be done to answer the question?

Yes, an increase in temperature is accompanied by an increase in pressure. Temperature is the measurement of heat present and more heat means more energy. Molecules in hotter temperatures move faster and more often, eventually moving into the gaseous phase. The molecules would fill the container, and the hotter it got the more they would bounce off the walls, pushing outward, increasing the pressure.
I suppose you could measure this with some kind of loosely inflated balloon and subject it to different temperatures and then somehow measure the size/pressure of it.