Temperature Lapse Rate or Why the Ice?

Flew an X-Cub out of Sedona, AZ, USA (KSEZ elevation 1472m) and climbed to an elevation of 2,800m and then descended into Flagstaff (KFLG elevation 2,138m).  The ambient temperature (reported by ATIS) at both airports was 17° C as it was mid-August, mid-day and one would expect it to be at least a bit warm.  The X-Cub (high performance 215hp version) had a terrible time holding any altitude above 2,000m and was very sluggish in flight.

Upon landing at KFLG I exited the airplane to discover it covered in ice!  ICE at an ambient temp of 17° C and an RH  below 50% - how can that be?

The standard lapse rate is 2°C per thousand feet (or about 6.5° C per 1,000m).   The lowest outside temp I saw while flying above KFLG at 2,800m was 11° C, which seems about right.

I had the weather set to "a few clouds" but carefully avoided flying thru any of them since I am only VFR qualified.  

SO - where did all the airframe ice come from?  There was none on the windscreen, which is why I was so surprised when I climbed out at KFLG and saw an inch of ice on the bottom of the engine cowl.  

And, sitting on the runway in 17° C sunshine - NO ice melted off in 30-minutes.  

This is the 2nd time I have encountered heavy ice in temperatures above 10° C in clear air.  

How does one fly a non-ice equipped GA plane when ice is formed in such benign non-icing conditions?

Can I somehow turn off ice effects since they appear to be inappropriately applied?

In this case - descending to an lower altitude where the ambient temp was 17° C did NOT melt the ice off the airframe - is that reasonable?

I bumped the ambient temp to 35°C and still had airframe ice 15-minutes later.