Yesterday, I had a group of three students attempting a more serious improv scene. It was about a mother and daughter about to attend a family reunion, and worried about rehashing the "issue" with Grandma from the last reunion. As the three characters began to interact, the student playing the mother came up with some really interesting stuff - how she talked to her mother, news she confessed to her daughter about Dad's dalliances, etc. But there was one thing the scene was screaming for: emotion.
It was obvious to me (and the rest of the group) that they were playing very cerebrally - thinking about their next line, thinking about how to respond to another character, thinking ahead to where the scene should go, thinking about how not to laugh at the physicality of the player playing the grandmother. It felt very corked - none of them wanted to take that chance and react emotionally. Particularly the mother - she was almost deadpan throughout.
I took the grandmother and daughter aside, and gave them one direction: when Mother tells you that Father has been cheating, react emotionally. I instructed the Mother to deliver her one line ("Honey, I need to tell you that your father has been cheating on me.") and then react appropriately to however the other two characters react. When the daughter reacted angrily and hurt, the mother in turn was able to react more apologetically and regretfully. And when the grandmother chimed in with her extreme disappointment, the mother turned to sorrow, burying her head in her hands.
It didn't quite get as emotional as it could've, and given them some real material to work with - but it was so much better. Most of these were junior improvisers, and tend to be much more reserved. It reinforced in me (and in some of them as well) the need to get out of their heads and to get them comfortable with acting and behaving with their fellow troupe members. How do we (our character) feel about what they've just heard, and how do we act upon those feelings? Don't just think it or say it, show it. Feel it. Some of the best improv I've seen my troupe do has been centered around themes with strong feelings - but only when they trusted each other enough to show those feelings and act upon them.
There are a handful of Emoting games that might help students get more into that "heartspace." Because the games tend to take emotions a little over the top for the sake of the gimmick, they may not necessarily bring emotional gravity to a scene - but they can at least get students emoting on stage. Emotional Roller Coaster is the one that probably best could be set up to carry a serious improv scene; for a little more fun, try Emotional Quadrants or Emotional Objects.