I would track down an oven industries controller. The controller should be able to react fairly quickly so building your own controller is probably not a good Idea. My understanding is you want the temperature higher than ambient. As KTP is a temperature tuned crystal or an angular tuned crystal all that matters is you hold one stable and adjust the other. Find an oven industries controller and make your life easy.
Pat B
laserman532 on ebay
Been there, done that, got the t-shirt & selling it in a garage sale.