@gunrunnerjohn
The attempt is being made to force the drive transistors into saturation. Thus the lack of heat sinks. However with the base pull ups, the H bridge dynamically brakes the motors when it goes to neutral. Ouch!
Interesting Lou, I didn't look that closely at the ones that have smoked here, but obviously something smokes the transistors, that's the part I've replaced a few times for these. I guess under some conditions the transistors don't go into saturation and dissipate a lot of heat. I've seen several that have cracked the plastic case, obviously lots of heat there. 
That makes sense, a NPN to drive one motor one way, and PNP for the second motor, the opposite way so they don't bind.
Actually, it's a little more complicated than that. The motors aren't individually controlled, they're in parallel or series, to drive them independently, you'd need two H-Bridge circuits.
There are four transistors (or other switching devices) in the H-Bridge, the object of the exercise is to swap the polarity of the motor drive. At any one time, two of the semiconductor switches is active providing power to the motor. To reverse direction, the other two are switched on and those are switched off. A fairly common failure of an H-Bridge is when a circuit failure causes one of the inactive switching devices to turn on, that creates a short and you get lots of current and heat.
Here's a pretty good description of a simple H-Bridge circuit using transistors. This one uses low current 2N2222/2n2907 complementary transistors, but the technique is the same for any size motor and semiconductor switches. This example also illustrates dynamic braking and coast provisions, depending on the state of the inputs. Note the cautions about conflicting inputs to the H-Bridge control inputs.
