This is one of those cases where I would spend the extra money to heat the water and wash as appropriate. There’s really three issues here.
One is that you need to reach a minimum temperature to kill mites, bacteria, etc. that thrive in bedding and undergarments. You can either wash in cold and then let the dryer take care of it, but when I work the numbers, it’s more expensive to fire up that dryer than to use the hot water and line dry. If this is not done, you will get transfer of bacteria (imagine face towels and underwear together).
The second issue is the effect on detergent and machine life. Avoid powdered detergents if you wash in cold as they won’t dissolve as well as liquids. You’ll also want to make sure you use a detergent specifically designed for a cold water wash. Many sources state you need to use more detergent, but this leads to other problems. If you do run mostly cold, it’s a good idea to run a very hot wash occasionally to try to flush out the buildup of ‘scum’ that will accumulate in the outer basket of the machine and to help keep seals and hoses soft. This stuff can get nasty in places you’ll never see, but will affect machine life. It’s also lead to the rise of “washing machine cleaner” additives.
The third issue is the chemistry of laundry. The idea is that you’re trying to relax the fabric so that the ‘pores’ open up to release trapped solids. This isn’t such a big deal on permanent press fabrics, but that hot water is needed for most things cotton. The mechanical action dislodges these oils and solids once the item relaxes and the soil gradually floats to the top. The spin prior to the first rinse in your Maytag is designed to spin this soil out to the outer basket, the following rinses work to dilute remaining detergent. At a 98.6F body temperature, those soils were absorbed/trapped. You really need to get above this to be effective. Any other temp requirement would be dictated by the detergent (there’s a lot more that goes into the actual chemistry and pH, but basically we no longer have the phosphates that helped take up the slack for poor temp or detergent, and enzymes do have some very specific requirements).