I think the TinyG could handle the motion part just fine, but the you might off-load the temperature stuff to the beaglebone. You might be able to write a reasonably simple program that controls the temperatures and translates 'E' words to 'A' words on the fly, and drive the TinyG with pretty standard G-code.
Maybe you could even make TinyG parse E words into A-axis words with one line around [
github.com]
A logic-level protected MOSFET like from [
reprap.org] should cover what you need on the power side, while on the sensing side you need only a thermistor and a pullup resistor to one of the analog inputs.
If separating Gcode for the heaters from the motion control might be more work than you want to do, you might buy a hardware PID controller and SSR and control the temperature manually. Or go for something from the
List of Electronics