What sony camera can output HDMI without recording for hours

Well I will test this on my camera. But since I am doing research for a broadcast setting it would be nice to know what cameras can do this.

Setup:
Will be either converting from HDMI to SDI with a blackmagic to wirecast computer or HDMI to RTMP to streaming services. Either way I need the camera to output HDMI while not recording. It will not be necessary to record because I will have external recording capability and will be streaming real-time. Will your sony output HDMI even if the EVF goes black. Plus if I don't record I hope to eliminate heating issues.

Test:
Should be able to do this with any HDMI TV. Connect HDMI output to TV and turn the camera on. Will the TV should the cameras picture for extended periods of time such as 1 or 2 hours?

Will appreciate the help from POTN family.

So you just need the camera to be in live view? Pretty much any modern camera will do that.

Only issue is the screen shutting off, dont know what the limits are on that. Or if it even has a limit while plugged in.

Yes live view. But without testing it I may purchase a camera (not for me) and the output doesn't stay on. That would be embarrassing.

Oh and lets not forget external power.

OK so I did setup my A6000 and with a setting that removes (can't remember at this moment) display info from the output it will remain on as long as the camera is powered. So with a permanent power source I should be good.