I'm running the app on a HTC One X and a Xperia tablet, both with Tegra3 CPU. So no info about the S4, sorry.
CPU temperature isn't shown by default, you have to set it on TempMonitor's settings.
But it's done quickly and the CPU temperature is shown immediately, so you'd install and try out it easily in that 15 minutes Google Play time.
For to try out the (simple) user interface you'd install the free version. It has an other icon (look for the dev's name) and doesn't support all of of these CPUs that the paid version supports. But maybe it supports the S4