I can tell you in the medical field their are no chips used that require more than a couple seconds to be fully functional. My wife works as a physician in the surgical field with robotic surgery and she stated if an emergency happens all equipment needs to be able to be transported set up and turned on in a very short time so a chip that requires 2 hours to work properly would not be used. And it sounds more like the programming needs to run its course more than the chip and the complex programming verse equipment capability of running it, forces the DAC to get bogged down and requires time to be fully functional.
There are different classes of equipment. A robot will operate correctly at startup just the same as a computer will (aside: DS DACS operate as accurately as they ever will at startup, no warm up required). A piece of high precision, high accuracy diagnostic equipment depends on digital data processing, as well as precision digital to analog and analog to digital conversions. There are a lot of diagnostic applications for precision conversions, and those probably take some time to come up to operating temperature. Stuff that medical professionals rely on for triage and emergency work has to function correctly the instant it is turned on, and it does. High precision diagnostic tools are used in a different environment. Ask your wife to find out if the lab rats leave their equipment on all the time so it works correctly.
The DSP software that comprises the megaburrito filter takes an input data word, compares it to the next word and interpolates between those to create intermediate values (upsampling). The filter is made up of about 18,000 transforms, all of which are hard-coded and can't change. The DSP chip takes input, runs the transforms, then give the result to the DAC chip(s). It does it the same way every time. When there is no input to the DSP it still sits there and interpolates zeros and passes them to the DAC chip(s). The analogy here is that the DSP is like the computer that runs the surgical robot: It does its thing exactly the same from startup to shutdown.
I tend to think about digital electronics as simple on-off devices, and they either work or they don't. The only thermal effect that I think about in digital electronics is overheating, and that results in a non-functional, possibly ruined, device. The actual transistors, resistors, capacitors, etc. in a digital processing chip are designed to function within a relatively large thermal envelope. Non-linearities don't matter because on is on, and off is off. Analog electronics are all about linearity, and temperature effects do matter. When it comes time to set the bias on some output transistors they have to be at operating temperature to get it right, for example. Analog audio stuff sounds different depending on the thermal state of the device.
Tha DAC chips themselves will give a different output depending on the thermal state of the chips. When I turned on my Mimby for the first time, sound came out as soon as it got done booting up. The sound got better after it warmed up. The difference in sound was because the DAC chip in Mimby was cold and did not put out accurate results. When it got to operating temperature, it sounded better.