Unfortunately it is impossible to hack a higher resolution onto a camera like that. You are probably thinking of the "Flir One" smartphone addon which uses a very low resolution thermal imager along with a 640x480 visible light camera, and blends the images from both cameras together to create a 640x480 output.
One thing that does bother me about the FLIR TCX is how they advertise an 80x45 resolution even though I'm pretty sure they used an 80x60 pixel Lepton sensor in the camera. I can't imagine why they would voluntarily leave 1/4 of the pixels unused on such a low resolution sensor, so maybe this is just a special 16:9 version of the Lepton sensor.