Low voltage transformers are the most important and expensive assets in a power distribution system. The life time of a mineral-oil-immersed transformer is decreased by raising the Hottest Spot Temperature (HST) in peak hours. This paper assesses the effect of load shaping through households' appliances scheduling on lifetime of a distribution transformer. An IEEE standard transformer is used to estimate transformer aging. This paper provides Demand Response (DR) optimization models to mitigate the thermal stress of transformers caused by overloading. Three smart home management strategies based on DR are compared and evaluated; In the first scenario smart home management is based on preference of customers, then real time pricing is taken into account, and finally the Loss of Life (LOL) of transformers are considered as an objective. To validate the three management approaches, realistic data for household load curves and device parameters are employed. Case studies and results reveal the significant impact of appliances' scheduling strategies on the expected lifetime of distribution transformers.