Don't worry, if you're like me, by the time you've dialed in your temp loss for the mash tun, you'll have moved on to wondering if your thermometers are accurate at all. Relax and have a homebrew. Grain wants to become beer.
I have a 10 gallon igloo that has an average temp loss of 6 degrees F when adding strike water alone. I generally shoot for 2 degrees over strike water temp, let the cooler warm up, let the water cool 2 degrees, then add grain when it's reached actual strike temp. Palmer's single infusion strike water equation from HTB seems to be fine for me from that point.
Unfortunately, every system will be different. My suggestion would be to heat your initial strike water above what you think you need, add it to your mash tun, record your initial heat loss, then wait for it to get to your strike temp. It wastes a little bit of time, but it allows you to see in real time the thermal inertia of your vessel once you are near mash temps. Keep some notes.
Disclaimer: I've had about 5 Georgetown Choppers by now, and may be getting more verbose than a sober me. But I can still spell "verbose" so that's good. YMMV. Hope that helps.
Toast.