A turbine engine cooling arrangement according to an example of the present disclosure includes, among other things, a core passage for receiving a core flow for combustion, a first airflow source including a first passage adjacent the core passage for conveying a first airflow, a second airflow source including a second passage adjacent the first passage for conveying a second airflow, and a heat exchanger that is thermally connected with the first passage and the second passage for transferring heat between the first airflow and the second airflow. The first airflow and the second airflow stream over the heat exchanger in a parallel radial direction and a parallel axial direction. An engine inlet divides inlet air into the core flow, the first airflow, and the second airflow. A method of providing cooling air is also disclosed.