Many astronomers are not aware that the Hubble Space Telescope is heated to about room temperature, and this is what led to the limited wavelength coverage of the infrared channel on WFPC 3. As a result, the highest redshift galaxies had to wait for confirmation by the JWST.
The technical reason for heating the HST mirrors involves the history of its technology, which was developed for spy satellites looking down at the Earth. The Earth is heated to close to room temperature by the Sun, and by heating mirrors to a slightly higher temperature the temperature could be stabilized and temperature gradients could be minimized. The Ultra-Low Expansion glass used for the mirror has a thermal expansion coefficient that goes to zero at this design temperature, so the mirror retains its shape. This technology is at least 60 years old.
When using HST to look at space, which has an effective temperature of about 4 K from the CMB plus all light from the stars and galaxies, a large amount of electrical power is needed to run the heaters. On the HST the heaters use about half of the 3 kW provided by the large solar panels. During the Origins Space Telescope study we found that it actually took less power to actively cool the mirrors to 4.5 K than to heat them to room temperature.
There is a small benefit from using a room temperature mirror, which is that it makes optical testing easier. Of course that did not work out so well for the HST. But the mantra of the space game is "test as you fly", not "fly as you test". Note that Schott Glass will sell ZERODUR mirror blanks that have zero thermal expansion coefficient at a cryogenic temperature like 95 K, and also metals like aluminum or beryllium have very small thermal expansion coefficents at temperatures less than 50 K. So JWST uses a beryllium mirror like the Spitzer Space Telescope.
JWST is a very sensitive telescope as a result of its large aperture and the very low background in space. The background radiation is emitted by the zodiacal light and the telescope optics, but the optics are passively cooled to below 50 Kelvin. The blackbody emission from a 50 K object peaks at about 100 microns and is almost zero for wavelengths shorter than 20 microns. Note that MIRI instrument actively cools its detectors, but the telescope is passively cooled. The interplanetary dust emitting the zodiacal light is heated to about room temperature by sunlight but it is very optically thin, so even though its radiation peaks at about 16 microns its intensity is about 3 million times less than the emission from a room temperature mirror.
The image below shows the backgrounds for a ground-based telescope, the HST, the Nancy Grace Roman Space Telescope, the JWST, and a cold telescope in space. The y-axis is logarithmic covering 10 orders of magnitude.
The WISE satellite performed a very sensitive all-sky infrared survey using a small telescope and detectors cooled to about 8 Kelvin using a solid hydrogen cryogen. The 40 cm WISE telescope was able to survey a large solid angle as fast as 6000 large ground-based 8 meter telescopes working in parallel could.
The NGRST will use a heated mirror due the history of its development. The 2010 decadal survey recommended the Wide-Field InfraRed Survey Telescope based on three white papers, and one of these was Stern et al. 2010 (I was a co-author) which proposed the Near-Infrared Sky Surveyor which would survey the entire sky in 4 bands from 1.0 to 4.2 microns, reaching a sensitivity 500 times better than WISE. But this science was lost when WFIRST adopted the "free telescope" from the National Reconnaissance Office, which used the HST technology. So the NGRST will do wide field surveying in the 0.5-2.3 micron range, but not 3-4 microns. Long ago I was part of a proposal led by Ed Ney for a first generation HST instrument that would have observed all the way out to the far infrared. It would have been severely affected by the background from the heated HST mirrors if the IR detectors available in the 1970's had been better. But IR detectors then were a million times less sensitive than currently available detectors, and the proposal was not accepted. I heard from one team member that Nancy Roman had said "[HST] will have an infrared instrument over my dead body."
Far in the future NASA hopes to launch the Habitable Worlds Observatory, a huge space telescope to characterize planets around other stars. This will have a huge starshade to block the light from the star. There is a concept where both the telescope and the starshade run at < 100 K. Since the starshade will take weeks to reposition in front of a star, there will long time intervals for general astrophysical observations, such as studying very distant galaxies. So a passively cooled HWO will produce better science than a heated HWO, and use tens of kW less electric power. I hope for the sake of future astronomers that NASA will not still be using 1960's spy satellite technology for the HWO in the 2040's.