I expect with some APDL code, you can implement temperature dependent convection. Hopefully, someone who knows how to do this will respond.
In the Mechanical APDL reference section is the MP command, which is used to define a temperature dependent material property, including Convection film coefficient.
There is an element LINK34 which can be used to convect heat from one node to another.
What is the physics behind the temperature dependent convection film coefficient?
What is the fluid that is convecting the heat away?
Another approach is to build a CFD model in Fluent and model the convective fluid flow. Temperature dependent properties can be used in Fluent.
By building a CFD model, you no longer need a convective film coefficient, the model will convect the heat using fluid motion.