We propose a mixed-integer nonlinear programming (MINLP) model for the simultaneous chemical process synthesis and heat integration with unclassified process streams. The model accounts for (1) streams that cannot be classified as hot or cold, and (2) variable stream temperatures and flow rates, thereby facilitating integration with a process synthesis model. The hot/cold stream "identities" are represented by classification binary variables which are (de)activated based on the relative stream inlet and outlet temperatures. Variables including stream temperatures and heat loads are disaggregated into hot and cold variables, and each variable is (de)activated by the corresponding classification binary variable. Stream inlet/outlet temperatures are positioned onto "dynamic" temperature intervals so that heat loads at each interval can be properly calculated. The proposed model is applied to two illustrative examples with variable stream flow rates and temperatures, and is integrated with a superstructure-based process synthesis model to illustrate its applicability. (C) 2017 Elsevier Ltd. All rights reserved.