Yes, temperature plays a crucial role in autolyse. The final resting temperature should be between 72-78 oF for achieving the optimum outcome. If the final dough temperature is very low, the enzymatic activity is slower and you might not get the desired results. Similarly, if you add very hot water for mixing the dough, or place it in a very hot environment, the enzymes get denatured or say destroyed.  So, yes temperature plays a crucial role in autolyse and the overall baking process.