A method of determining characteristics of fluids flowed between a wellbore and multiple zones intersected by the wellbore can include measuring a first distributed temperature profile of the fluids along the wellbore while the fluids flow in one direction through the wellbore, and measuring a second distributed temperature profile of the fluids along the wellbore while the fluids flow in an opposite direction through the wellbore. Another method can include flowing the fluids in a first direction through an annulus formed between tubular strings in the wellbore, measuring a first distributed temperature profile of the fluids while flowing the fluids in the first direction, flowing the fluids in a second, opposite direction through the annulus, and measuring a second distributed temperature profile of the fluids along the wellbore while flowing the fluids flow in the second direction.