Malware would need to be stored somewhere first. This is in fact possible ... on TV's and bluray / DVD players that can cache an Internet content.
However, malware would need to alter the code....to do real harm. There's the firmware that can be flashed. The firmware file size is rigorously checked first for the correct size AND bit sequence. I suppose if someone is bored enough, then YES, the malware could flash the firmware chip and render the TV inoperable (or make it do silly things!... I can see how this could actually be quite interesting and challenging)
There are other codes that operate certain functions inside the TV - these codes are PERMANENTLY burnt on certain chips so malware can not do any harm here for example, the T-CON processor knows which memory area to use to store the incoming frame, knows how to deal with next consecutive frame and how to compare the two, and knows how to generate / interpolate the intermediate in-between frame to smooth the motion. These sets of commands are permanently burnt and can not be corrupted by malware.
I can't really see the incentive in writing the firmware that would make TV unusable but you never know
Boky