It's Not Hot Water Per Se, Nor The Lack Of It
But one needs something to help "sanitise" one's washing to deal with any bacteria/odors.
Problem with most liquid laundry products is they do not contain bleach, and using hot to boiling wash water can cause excess froth.
On the UK/EU side of the pond a good detergent with a built in bleaching system, or added on it's own should solve the problem. Both sodium percarbonate and sodium perborate both release oxygen in wash water, which in turn helps deal with "germs" and odors. Activated oxygen bleaching sytems go one better in that the peracetic acids formed are a stronger bleach and disenfectant than plain hydrogen peroxide at wash temps <120F.
If the whiff is due to mould or mildew, even the hottest water alone may not due as such things form spores to deal with inhospitable conditions, and quickly come back to life once things are good.
For the above you need something that kills mildew/mould. Some chlorine bleaches, oxygen bleaches, peroxide, quats, UV light, etc.
If the towels are coloured, washing at temps >140 with oxygen bleach can cause fading.
Personally have found that once an item has been subjected to any of the above, and still has a whiff about it, then into the rubbish it goes (yes, sad and wasteful, but consider time and product cost in trying to rid them of the whiff instead), and purchase new.
IMHO much like knickers, drawers and bed linen, the only satisfactory colour is white, in either pure cotton or linen. Such items can be washed the daylights out of if required, and if well made, not suffer badly.