For DADS50
Hope this helps...
Sounds like your heat riser is opening and closing which is good.
I can only guess that there may be some interference between the accelerator rod and the thermostatic spring. On my 55 series two these parts are very close together. Removing and installing my spring brought this to light.
If your engine is warm, the valve should stay OPEN whether giving gas or not. However, it cools off quickly and if it was only an "idle warm up" you may have not gotten it warm enough to stay open.
I think Denny Graham can help you more than I can. His answers really set me straight.