I ran the engine I had just re-built last spring for more than 3000 miles last summer using Castrol 10W30. It ran fine. I changed the oil last fall, before I put it away for the winter and it is ready for another summer of hot driving - again with Castrol 10W30.
If your oil pressure is more than 20 or 30 psi at idle when the engine is hot, that's fine. If your oil pressure when driving at 50 or 60 MPH is 45 to 70 psi, that's fine as well. If your pressures are lower than the values above, then switch to 20W50.