It has been pretty thoroughly studied, and chickens definitely have their sex determined by genes, not temperature.
All birds have sex chromosomes Z and W. A male has ZZ, a female has ZW.
Chickens, turkeys, ducks, and geese all have some color genes on the Z sex chromosome. Matings can be set up where the father has a recessive gene and the mother has the dominant gene. This gives daughters who show the recessive gene (because they inherited it from their father, and inherited a W chromosome from their mother). And sons show the dominant gene (because they inherited the recessive from their father and the dominant from their mother.)
Because the genes on the Z chromosome can be used to produce sexlinks in this way, and it does work reliably, we have pretty good evidence that sex is determined by the sex chromosomes and not by temperature.
