H_Bridge with PWM gets too hot
Short answer: You're drawing too much current through the H-bridge.

Longer answer: The H-bridge is most efficient when fully on and that's when the chip gets rated for the maximum current. The rating also, probably, states that a heat sink is attached to the chip. Using PWM to slow down the motor decreases the current going through the bridge, but also incurs inefficiencies because the transistors / MOSFETs are partially on, and thus acting somewhat as resistors. This inefficiency manifests as heat.

So you have several options.
1. Choose a smaller motor.  This reduces the overall current needed.  Only feasible if this is a learning project.
2. Choose a beefier H-bridge.  This increases the ratings of the bridge to handle current for this motor.
3. Add a heat-sink to the existing bridge.  This will help dissipate the heat generated.  

Generally I'd recommend both 2 and 3, but it depends on your ultimate goal of the project.