I have a Dynex DX-37L150A11 that begins buzzing extremely loudly after approximately 45 minutes of use. This buzzing persists even when I plug in external speakers or headphones. Additionally, the buzzing noise does not depend on the volume the TV is set at. It starts out relatively quiet, and within a minute it is ridiculously loud; overwhelming all sound. The picture remains intact. If I unplug the TV for 5 minutes, I can get another 45 minutes or so without interruption. This occurs no matter what input I am utilizing.
Sounds like something in the TV is generating the noise after heating up after 45 minutes.
You could try replacing the audio board but on a Dynex parts would not be readily available.
A technician would wait until the noise started and then use freeze spray to try cooing down parts (maybe on the audio board) until they found the one that is the problem.
Whether the cost of repair would make sense would depend on your situation.
You could use an external HDMI input selector with audio extraction to bypass the TV for powered speakers.