In my opinion, the idea of a HERMS system is to regulate the temps in the mash for the duration of the mash.
If your HLT (I take it that is where the coil is in your situation) is not up to temp yet - do not mash in yet. Although I cannot understand why it is not. In your world the mash water (before grains added) temp should be in your HLT temp. Then you take the cover off, start the pump, and wait for it to lose it's greater temp value than your mash tun after you add the grains. It should take just about 5-10min...
I typically mash in with water from my HLT which sits at 159-166F depending on what you are striking in at (I aim at 149-156F) due to the grains being at room temp and depending on your total lbs in grain you need to account for that loss in temp when you strike in. The more you do it - the more you will get accustomed to what happens...
It is late here and I may be brief but I hope this helps...