If you absolutely must play Temple Run on a Sony handheld, the is your best bet. Because the Vita has a touchscreen and much more power, it can run the Android version via unofficial "wrappers" (though this requires a hacked Vita and the original Android .apk files).
There is no official version of Temple Run released for the PlayStation Portable (PSP). The game was originally developed by Imangi Studios for iOS (2011) and later ported to Android, Windows Phone, and other touch-based platforms. It was never officially ported to the PSP. Any ".rar" file claiming to be Temple Run for PSP is almost certainly: temple run for psp versionrar link
file online claiming to be a PSP version of Temple Run, it is almost certainly one of the following: Fan-made Homebrew If you absolutely must play Temple Run on