So, we have an HP Pavilion tx2617 (tx2500 series) tablet computer. A while ago, it started to reach critically high temperatures and shut down. The fan is running all the time at high speeds, making it a very noisy fan. I tried a few things, including reducing the processor speed of each core to 1GHz (rated up to 2GHz). This helped a little, but as you may guess, the correct solution was to clear the vents of dust. A can of compressed air used in the corner vents returned a normal air flow and thus sane temperatures to the laptop. Hurrah.
Relevant Hewlett-Packard support details. This marks the first time that dust collection has actually resulted in heat issues for me. Neat.