Getting around not having a heater
Industrial/commercial laundries did or do this by simply having several changes of water after short cycles.
After a cool/cold flush, there is a warm pre-wash, followed by two to three "suds" baths in hot water (140F-160F)lasting 7 to 10 minutes. Then comes a first "hot" rinse (which is usually the chlorine bleach bath if that is being used), followed by two more hot rinses, then one or two warm rinses with final or preceding making up the starch, fabric softener, sanitizer, antichlor or whatever else, then extract.
If relying upon chlorine bleach for sanitizing the wash, then reaching and or maintaining very hot to boiling water temps (160F to 180F or above) isn't strictly necessary. Chlorine bleach will whiten, remove stains and disinfect/sanitize perfectly well in cold, cool, warm or hot water. Things slow down a bit at lower temps, but job is still done in five minutes or less.
If you don't let washer cool down, at some point latent contained heat is enough to keep successive changes of water from cooling down much. Many commercial/industrial washers then (and still now) don't extract between bath changes, so there is considerable carry over of hot water between cycles.