Many battery apps will give you the internal battery temperature. I've also heard that some battery apps can cause issues with 4G phones, though I can't personally confirm this.
I use an app called Phone Info which gives a lot of info including the battery temperature.
On my old Palm Pre, I had a homebrew apps that gave battery temperature and CPU temperature. They were never the same. Some things caused the battery to heat up and some things caused the CPU to heat (overclocking, for one). Would be nice to have an app that showed the battery and CPU temperatures but maybe the GNex isn't capable of measuring the CPU temp?