Follow up....
The Ray Allen T2-7A servo has been operating the cowl door for about one year now. Recall that RA doesn't claim their servos will hold up at the sort of temperatures typical for a well sealed cowl, but they don't say they won't either. So far, I have not noticed the slightest reduction in performance, increase in noise, or any other symptom of a heat issue. It is insulated with fiberfrax felt and aluminum tape, and it is shielded from exhaust pipe radiant heat. The insulation just means it takes longer to reach the overall in-cowl temperature, so it's living with the heat.
The drag reduction is nice, although a fully closed door requires an OAT at 65F or so to maintain oil temp below 200 in fast cruise. Here's a current example; yesterday, hauling back to the office after a truck sale in Mississippi. It was warm at 7500, about 66F, and I'm at best power mixture, door closed, and 69% power per the EFIS. True airspeed checks per the NTPS method say the EFIS is accurate.
With this exit geometry, door position has strong effect on oil temperature, or more precisely, oil cooler mass flow. Given the above conditions, opening the door about 1/3 will lose 1~2 knots and drop oil temp 6~10 degrees. That's rarely necessary if I get high enough, as OATs in the 10K ballpark tend to be low enough for a fully closed door.
Down low in a hot day, full open costs about 4 knots in cruise, and puts oil temperature under control of the vernatherm, about 187F for mine. Obviously the door is full open for climb, or crawling around in slow flight. Yesterday it was over 90F on the ramp at KPIB. With the door full open, taxi time and a WOT/2700 climb to 5500 @125 IAS didn't break 200F.