The fungus wants warmth to spread and cool to fruit. ICAR-DMR's species table puts spawn run at 22 to 25 °C and fruiting at 14 to 18 °C. Hold the first band until the compost is colonised, then move the room into the second.
The drop is not a small adjustment. With fresh air and lower carbon dioxide it is the signal that tells mycelium to stop spreading and start fruiting. A seasonal grower in the plains gets that drop from winter itself. A controlled farm buys it from a cooling unit. Both are managing the same biology.