In recent years, user's trust has gained attention in recommender systems. Trust plays a vital role in the recommendation of online products. Trust is a dynamic feature which evolves with passage of time and varies from person to person. Trust-based cross domain recommender systems suggest items to the users usually by ratings, provided by similar users, often not available in the same domain. However, due to the sparse rating scores, recommender systems cannot generate up-to-the-mark recommendations. In this research, we solved a user cold start problem, mainly by modeling preference drift on a temporal basis. We tried to solve this problem by adopting one of the scenarios of cross domain of 'No Overlap' using cross domain information. In this work, we proposed a model called Trust Aware Cross Domain Temporal Recommendations (TrustCTR) that predict the rating of an item about an active user from the most recent time. We generated user features and item features by using latent factor model and trained the proposed model. We also introduced the concept of trust relevancy that shows the degree of trust, computed the trusted neighbors in target domain for an active user belonging to a source domain, and predicted the ratings of items for cold start users. We performed experiments on public datasets Ciao and Epinions and used these datasets in cross domain form such as the categories of Ciao as source domain and Epinions as the target domain. We selected five different domains, having a higher proportion of rating sparsity, for observing the performance of our approach using MAE, RMSE, and F-measure. Our approach is a viable solution of cold start problem and offers effective recommendations We also compared the model with state-of-the-art methods; the model generates satisfactory results.