This is not true. The sensor should not be damaged by such use. The phones temp will be fine so long as it is in cool conditions (i.e. 72 degrees or so).
DSLR's do not limit to 12 minutes because of sensor issues. It is due to file size limitations. All of the popular manufacturers utilize FAT32 for memory card formatting, which doesn't allow a single file to exceed ~4 GBs in size. Therefore, due to compression type and bitrates chosen, they simply reach the max file size within 12 minutes.
Panasonic micro 4/3 mirrorless DSLRs are able to exceed the file limitation by creating separate chunks that get automatically stitched back together seemlessly. Canon and Nikon haven't worried about the problem, and therefore haven't employed a similar technique.