I've read the thread, and shuddered at the thought of changing the circuit electronic time constant(s) without fixing the problem. I believe that Fred Bloggs & Jim Thompson have nailed at least the first point of failure to pursue. The fact that you are blowing cold air at time T2 indicates that the sensor or circuit is not turning off the blower when the temperature in the plenum drops. You need to fix that first, then address the other problems, like too often cycling, if any remain.
Ed