We present a microfluidic device for rapid and efficient determination of protein conformations in a range of medium conditions and temperatures. The device generates orthogonal gradients of concentration and temperature in an interrogation area that fits into the field of view of an objective lens with a numerical aperture of 0.45. A single Förster resonance energy transfer (FRET) image of the interrogation area containing a dual-labeled protein provides a 100 x 100 point map of the FRET efficiency that corresponds to a diagram of protein conformations in the coordinates of temperature and medium conditions. The device is used to explore the conformations of alpha-synuclein, an intrinsically disordered protein linked to Parkinson's and Alzheimer's diseases, in the presence of a binding partner, the lipid-mimetic sodium dodecyl sulfate (SDS). The experiment provides a diagram of conformations of alpha-synuclein with 10,000 individual data points in a range of 21-47 degrees C and 0-2.5 mM SDS. The diagram is consistent with previous reports but also reveals new conformational transitions that would be difficult to detect with conventional techniques. The microfluidic device can potentially be used to study other biomolecular and soft-matter systems.