In this paper, we propose and study the effectiveness of customer engagement plans that clearly specify the amount of intervention in customer's load settings by the grid operator for peak load reduction. We suggest two different types of plans, including Constant Deviation Plans (CDPs) and Proportional Deviation Plans (PDPs). We define an adjustable reference temperature for both CDPs and PDPs to limit the output temperature of each thermostat load and to control the number of devices eligible to participate in Demand Response Program (DRP). We model thermostat loads as power throttling devices and design algorithms to evaluate the impact of power throttling states and plan parameters on peak load reduction. Based on the simulation results, we recommend PDPs to the customers of a residential community with variable thermostat set point preferences, while CDPs are suitable for customers with similar thermostat set point preferences. If thermostat loads have multiple power throttling states, customer engagement plans with less temperature deviations from thermostat set points are recommended. Contrary to classical ON/OFF control, higher temperature deviations are required to achieve similar amount of peak load reduction. Several other interesting tradeoffs and useful guidelines for designing mutually beneficial incentives for both the grid operator and customers can also be identified.