A BBQ grill has no insulation, and heat would be very irregular. Opening it would dump all the heat , so you would be trying to heat the void back up again after placing in the blades. Also, the gauge on a BBQ is VERY inaccurate. It may vary by 50-75 degrees, and only reads the temp at the top of the hood. The temp at the grates would be very different.
Ah fair enough.
For tempering you need an insulated box with a het source. A toaster oven will work on the minimal side, and they can be converted by adding some insulation and PID control to do small knives pretty well ( see PID Controlled toaster oven in the stickys). A kitchen oven with a digital meat thermometer by the blade can be set to get pretty good tempering control.
Will check those stickys!
I suppose a crafty guy or gal could take the bottom of a BBQ grill and add a insulated top with an end door to insert the blades, a circulation fan for more even heat, a PID control for the burners, etc. … but it would be an expensive task to get a fairly poor tempering oven. ( and you couldn't cook a steak on it anymore) I bet most folks could get a small used oven ( gas or electric) for little or nothing and have it in the shop to use for tempering only. This would allow putting in steel plates on the shelves for thermal mass, and adding some TCs and readouts to keep track of the temperature of the blade.