Actually no, the heat needs to escape to keep the temperature under control. The temperature is what has to be kept in the proper range for Fusion to occur at the planned rate. I don't know as much about control of fusion reactions as I'd like, but I think the reaction rate is highly temperature-dependant, so we'll want to keep the temperature in a tight range. Too low a reaction rate, and the plasma cools down too much and would have to be re-heated externally; too high and you might burn up fuel faster than you can resupply it, causing what I guess you would call a stall, also requiring a restart.
All of the reactions we've generated so far have a low to nonexistent reaction rate, because the reaction generates lots of heat, and the research reactor designs we're using don't have a way to extract that heat at power-generation levels. To build a power reactor, we'll have to maintain the reaction temperature, at which massive amounts of heat are generated, and extract that heat to keep the temperature stable.
Designing the heat transfer for that is sure to be fun. I don't know the temperature of the burning plasma, but I'm sure it's insanely high compared to any kind of conventional material or process. So somebody has to design a system to transfer GigaWatts of heat from a burning plasma at effectively infinite temperature to some perfectly ordinary water at a controlled rate without melting anything.