So does the pi 3 if you stick it in a case, even with a heatsink.
I was using a pi 3 with a heatsink in the official case to play a h265 movie (which will be software decoded on a pi3). After about 10 minutes I noticed it started dropping frames and it displayed the thermometer symbol in the top-right of the display.
When I removed the top lid from the case, the temperature dropped enough for the thermometer icon to disappear and playback to continue smoothly.
Over the years I've used Raspberry Pis as little media players, but they kept burning out every 3-4 months; the card reader (their SSD) wouldn't work, or they'd just blink some other error message. I thought they were just cheaply made ($35 after all). Anyway, long story short, I got a fan and the last one has been working for over a year without issues.
You can mitigate this somewhat with https://github.com/azlux/log2ram
With some finagling you can get them to boot an OS from an external disk then your SD card can just hold a read-only boot loader.