... in Madrid Thursday, May 11 through Wednesday, May 18 ... 15-day forcast now shows that it will be much warmer than normal ...
Low to mid 80's (27-28 Celsius) isn't all that warm for Madrid in May. It should cool down nicely after sunset. Do most of your tourism in the morning; after lunch do the
siesta bit, then you'll be 'Geared up' for going out in the evening. Rudyard Kipling wrote: Only mad dogs and Englishmen go out in the midday sun. But if you want to include a
Corrida at
las Ventas be prepared to suffer.
We really want to be able to wear shorts -- is that OK for walking around and going to museums? ... When is it NOT OK to wear shorts/t-shert?
You are asking two questions: one about shorts and the other about t-shirts. Walking shorts tend to be more acceptable during peak Tourist season (mid-Jul to mid-Sep), but Madrid during San Isidro is also considered 'high season.' I don't think tee-shirts or tank-tops should ever be worn as an outer garment. A light, cotton shirt is more acceptable (or a golf shirt, with collar).
... we'll be in Segovia ... and in Toledo ... Do the temperatures in those places vary much from the Madrid forecast?
No. But in general I think you are putting too much faith in a 'forecast' (actually an outlook) for fifteen days in advance.