Purplpixie

Works best with yellows oranges and reds. May turn blue gray, just warning you. Yellow orange and red are usually iron, it sure changes.
Yellow to orange
orange to red
red to redder or into brown.

Some browns turn lavender.
But all of the above is not for sure, you never know what color the stuff will change.
Cause there is many metal salts. and salt presence turns black
This batch was wacko, it was bland before I cooked it, and no black

I would cook that in a second. To see what the lavender/reds do. Mind you, that is beautiful as it is.
Tough competition w/out heating. Awesome agate spirit.

Some coral had white skin, from sitting in white clay. Often lacks iron, so little color change.
Those found packed in red/brown clay often go wild.
Those found in saltwater clay will go black-for sure, usually around the edge, depending on porosity of agate.(see slabs in last photo)
Many effects from the soil the agate formed/resided in.
Your agate has a brown skin, good sign. And lavenders are rare for me, but lavender almost always gets deeper lavender.

That is a very high grade of glassy agate. I would think hotter than 500/550F is hot enough.
If it came out of wet conditions you will want to leave it where it can dry, like over the furnace below 210F.
Hotter than 212F, and it can break the rock if heated too fast. Gotta get rid of the moisture slowly.
I pile the coral in the sunny side of the greenhouse, after a year I do not have to preheat it.
Otherwise, I preheat it for 24 hours in the furnace at 200F.

Damn it,now I'm droolin"!!!!!!!

The agate can become even darker in purple.  To get into the seam of the high grade material, you need to dig at least a few feet through topsoil , forestfire ash and colored volcanic ash layers. The area is as dry as??? California close enough to a description. 
I have a lot of the blue, resembling the Buse lake agate I posted if its still up, probably not, that's what I want to give it a try with first. Getting the feeling it wont enhance the blue only turn more grey. Still have to give it a shot to find out. Keep u posted when I pick up a sandbag, ground is solid cant dig it up and give it a shot on the BBQ.
500 to 550, got it memorized. Slow gradual heat to 500 then bake for at least 1 hr. Gradual cool down...say 150 degrees every hr? to heat off?
Thanks.

Harley uses a turkey roaster to heat treat his rocks, layered in sand and ramp it up to whatever temp he needs and then ramps it back down by 50 or 100 degree increments.

T shirt weather
Sounds fun to me

Actually you can take the thermostat apart and get it to go higher but that is best left to people who know what they are doing.

Probably tweaking the bimetallic spring. After that adjustment, fire proof location sounds safe.