I have a gas-fired BIAB system with a steamer basket in the (11G) kettle about 2" above the bottom, a pump, and recently had to replace my sight glass, so got a T for the sight glass with a temp probe reducer.
I have almost the same system design but bagless. My mash tun pot is about 11g and wort circulates from the bottom through a sieve plate about 1 1/2" off the bottom, through the grain bed, through a top sieve plate, over flowing back into the main boiler (in which the mash tun sits). This is a two bucket system with the tun bucket sitting inside the main boiler bucket. I affectionately call it my "brew in a bucket" BIAB.
The main boiler is gas fired and temp is electronically controlled from the pump outlet which feeds the bottom of the mash tun. The pump's wort source is from the bottom of the main boiler. So circulation is: boiler bottom.. pump.. tun bottom.. grain.. tun top.. boiler top.. etc.
The flow is sampled immediately after the pump as it's forced into the bottom of the grain bed. I monitor the top of the grain bed at the output sieve with a second thermocouple which now gives me tun input and output temps.
In operation I find that once the main boiler temp reaches the set point, it takes about another ten minutes for the tun output to stabilize at that temp.
I had to experiment with the flow rate in this system to prevent peculation and channeling. Once I learned to slow things down to manage the channeling I discovered my temps fell inline much more quickly. Not sure I fully understand why but since I discovered this, my system has been a jewel to brew with.
For mashing at 152*F I typically heat my water to about 156*F, readjust the controller to 152*F, mash-in which typically drops the temp to a couple of degrees under the target. Wait about 10 minutes for the target temp to recover to the 152*F and start my mash clock. After that it takes about 10 minutes to see the top TC attain the 152*F. From that point on the mash temp doesn't vary more than about 1/2 degree from the target temp, at either TC.
So, this was a rather long way to suggest you play with your flow rate to optimize your temp control.
Cheers....