The wood will be warm from the warmed soln application of the oxalic acid while you are brushing it on or dunking the wood into it.
No need to warm up the wood itself in any way like under a light bulb or with a heat gun, ect. At least I've never done that or seen the need to.

The stock will cool off of course when you flush the stuff off.
The main thing is to just be extra careful with the wet wood. It dents and bruises very easily.