even though it will eventually grow cold and die it WILL continue in motion forever.
http://www.astro.ucla.edu/~wright/cosmology_faq.html#bestfit
Will the Universe expand forever or recollapse?
This depends on the ratio of the density of the Universe to the critical density. If the density is higher than the critical density the Universe will recollapse in a Big Crunch. But current data suggest that the density is less than or equal to the critical density so the Universe will expand forever. See Part 3 of the tutorial for more information.