I used to be Team Heat, but am learning to live without it myself and have found success with the following...
After washing and conditioning my hair, I use a microfiber towel to absorb excess water from my hair for 1-2 hours. Then I style my hair in plaits to airdry. I usually do this in the early evening right after work if during a weekday so I can avoid blowdrying my hair. In the morning once it's completely dry, I unravel the plaits.
Now on the first day, the style isn't going to be the length or shape that I exactly want due to shrinkage, so I'll put my braidout into a low/side ponytail or bun during the day and rebraid at night.
Once my hair has been stretched out over the next few days, I can get away with putting my hair in a high bun instead of rebraiding at night until my next wash day (which is every 2-4 weeks).