After resin infusion, and the part is cured at room temp. do you have to cure it in an autoclave to insure that the part doesn't deform, delaminate or get soft in the sun....?

No. The autoclave would be used during initial cure. It would by pressure, consolidate you stack more densely. Therefore less resin more fiber ratio and so a stronger part. What you can do is heat your cured laminate to 250f for an hour or so and the estimates I hear is a 20% strength increase can be had.

Fred 

A postcure will improve the properties of the end product. 

Also once the infusion has been done, if you dont postcure then in reality there will still be resin that hasnt fully cured hence the need for a postcure at elevated temperature.

Sure eventually it will fully cure itself but you are looking at months in the cool british climate.