What model Little Giant?
I successfully used STC-1000 on two LG 9200, one forced air and one still air, with much better performance than the LG controller.
One thing to keep in mind is that you need to turn the knob on the LG all the way up so that only the STC-1000 is controlling the temperature.
STC-1000 are also of very low mass, especially without a turner. If not using a turner, use a full bottle of water to act as a heat sink to help stabilize temperatures. Small, smooth gravel in the water channels can help too, and can be sanitized between sets by boiling.
Where do you have the sensor mounted?