This topic keeps coming up, and every time it does someone else becomes convinced of the benefits of a Tilley hat for hot weather Morganeering. I've had mine for just over a year now, and it's flippin' brilliant.
Give it another couple of years and it won't be a question of "Which hat do you favour for driving your Morgan?" but "Which model of Tilley do you prefer?".
If there's anyone out there who still hasn't discovered just how good these things are, I urge you to give one a try.