It looks like a custom heatsink on that mobo. A standard desktop heatsink for AM2/FM2 won't work because there is no compatible heatsink retention hardware.
I agree with neon. You are pretty much stuck with the original APU Heatsink and fan.
The only thing that you may be able to replace is the heatsink fan. If you purchase a larger CPU Fan, you won't be able to attach it to the CPU Heatsink. If you can find some way of attaching a larger CPU Fan without using screws and the new Fan size won't interfere with any other components on the motherboard or attached to the motherboard and it can be powered from the CPU FAN motherboard plug then that will probably be your best bet. Maybe you can use plastic wire ties to hold the large fan to the heatsink if you can find a way to anchor the wire ties to the motherboard and heatsink.
Seems like the heatsink is doing most of the cooling with the fan helping to circulate cooler air around the heatsink.
Try increasing the airflow in the computer case which should aid in cooling the cpu better and also everything else in the Computer case.