Generarly speaking the transconductance depends on process and temperature, even if you have a fixed current. When simulating your circuits you must include the variations on the bias current.
I don't know if you are referring to this, but there is one circuit which generates a bias current, whose variations with process and temperature variations make the gm of transistors biased with that current be almost cte.
However this is only true if the resistor used on that circuit does not have variations (basically you must use an external resistor with low tolerance)
Regards,
PS: The circuit that I mentioned can be found on David & Johns Book