ECMO is half of "Mechanical supports: ECMO/IABP", an L1 topic of Section 2.1.4 in the second edition of the CICM Syllabus for the Second Part Examination, and the waterbath heater is such an unglamorous and stable part of the ECMO experience that it seems almost a pity to dedicate an entire chapter to it. There's not even enough to summarise for a little "grey box" breakdown of the chapter. But on the other hand the absence of this device, or its sudden failure, would be spectacularly terrible in a way that would immeditely remind you of its importance.
Fairly, the HU-35 brochure and user manual is the best resource for this device (a "widely used" system), but if you want to refer to a more generic discussion of the heating or cooling needs of an ECMO patient, the discussion section from Bilodeau et al (2024) is an easy to read dissertation on the decisonmaking about which unit to use by the article authors, as well a comparison of three commonly used appliances.
To be unfairly simplistic, this thing is usually a simple kettle with a pump and thermostat, functionally indistinguishable from enthusiast-grade aquarium equipment. The local HU-35 is capable of delivering a maximum of 500W of heat, and is said to pump with a 10 W pump at a maximum flow rate of 5L/min, which makes it suitable for a 350-400L tropical tank full of sensitive Cichlids. The water pipes connect to the oxygenator with attractive blue tubing:

It is important to note that this device cannot cool. But considering how frivolously an ECMO patient squanders their joules, this may not be a problem, even if rapid cooling is desired. Mojoli et al (2015) measured the power consumption of a heater and equated that to patient heat dispersion (total heat of the system remaining stable) and concluded that the circuit must lose heat at a rate of 58 ± 12 W when everything is stable and the flow is 3L/min. In other words, when a human body produces 100W of heat at idle rest, it remains at a stable temperature, and when you add an ECMO circuit into the picture, an additional 58W needs to be contributed to maintain a stable temperature; ergo the unheated circuit would be cooling the patient with an energy deficit of -58W. Considering the human body has a specific heat of about 2.98 kJ per kg per 1°C, it would take the dispersion of 208,600J of heat energy (70× 2980) to cool a 70kg human by 1°C, which would occur over about 60 minutes (as 1W = 1J/s, i.e we are losing 58J per second, and it would take 3596.5 seconds, or 59.94 minutes, to completelty burn through 208,600J). In short, when asked "how fast can the ECMO circuit cool a patient", one could confidently blurt the factoid, "by 1 degree per hour".
What could go wrong, you ask, looking at a piece of industrial-looking machinery with a dependable heft (about 15kg) and reassuringly 198os scifi-looking glowy numbers. Surely this could never fail in a million years. Indeed, reader, these are not particularly temperamental, as far as ICU equipment goes, but they can still cause problems, some of which are listed here along with solutions thereto:
Shrimpton, Nicole YR. "Evaluation of disinfection processes for water heater devices used for extracorporeal life support." Perfusion 34.5 (2019): 428-432.
Bilodeau, Kyle S., Kevin Charette, and D. Michael McMullan. "Safety and efficacy of extracorporeal membrane oxygenation heating units." World Journal for Pediatric and Congenital Heart Surgery 15.1 (2024): 30-35.
Stroming, Jeremy, and Dava Newman. "Critical review of thermal management technologies for portable life support systems." 49th International Conference on Environmental Systems, 2019.