I'm also having this problem. I'm using Airmail 3.5.4 on a late 2015 MacBook Pro. The only thing that I've done is cleared the message cache recently and I think this is when this started happening. It uses so much energy I need to quit it and use Mac Mail when on battery so that it doesn't drain it too quickly.
Using Airmail 3.5.4 (467) on Macbook Pro 13" mid 2010 with MacOS Sierra 10.12.6.
Airmail is draining battery and heating up laptop with a constant usage of % CPU over 100%. Right now with 146.4%.
It has been happening over the last 3-4 months every single time I start up Airmail.
I haven't been able to find any fix anywhere apart from the comments on this thread.
If I do not find a fix I will have to stop using Airmail immediately.
I am also having this problem. Airmail 3.5.9 on Macbook air early 2015. The Support Staff response here is not helpful as we are all saying that the laptop heats up even after the initial fetch. It is constant. Mine is right now at 201% and Airmail is idle.
I am running App Tamer to monitor CPU usage for various apps. My Airmail 3 (current update) on my 2017 5K Retina iMac is using only .01 % of my CPU at rest and about 30% when downloading mail then drop down to .03 to .01% of my CPU. RAM usage I regard as a bit high currently at 463 MEGS at rest.
Same problem for me - just started yesterday. Tried updating to Version 3.6.1 (506) but that hasn't helped. Airmail starts off at reasonable CPU level but then builds and builds, eventually becoming unresponsive.
Using an old macbook (2010) running Sierra (10.12.6).