Appliances that cycle on and off throughout the day, such as fridges, freezers, and air-conditioners can collectively provide second-by-second electricity supply-demand balancing known as frequency response. Previous studies have shown that deterministic temperature set-point control of a homogeneous population of such appliances can cause herding behavior with detrimental effects on the system. Here, we use computational modeling to establish the minimum population heterogeneity required to prevent herding problems without requiring centralized or stochastic control. We discover a linear relationship between the benefits that fridges can provide and their number. The impact on system benefits and on fridge temperatures of varying fridge frequency sensitivity is also explored, and a viable range for sensitivity (the control parameter) is proposed. Our approach involves simulating a large heterogeneous population of frequency-sensitive fridges using 12 months’ GB system data from National Grid. We compare the historic frequency response from other response providers with their response in our fridge simulations to determine the benefits of the fridge population response. We find that a fridge population can offer a valuable demand-side response service to the electricity system operator, requiring neither the expensive infrastructure of centralized control nor the regular intervention of stochastic control for temperature cycle desynchronization.