I think the '38 mounting is similar to the '37. I just had my 1937 apart and this is the arrangement:
The radiator is attached to the rad shell by (6) bolts through sheet metal brackets mounted on the sides of the radiator. There should be captive nuts in the rad shell at the bolt locations.
The bottom of the radiator should not contact anything. The red shell is mounted to the frame cross member using two long stovebolts, The bolt heads are quite shallow and the square bosses under the heads locate in the slots in the bottom of the rad shell. There is no gasket between the bolt head and the rad shell and there should be lots of clearance between the bottom of the radiator and the U shaped channel in the rad shell where the mounting bolts are located.
There are rubber cushions between the rad shell and the crossmember, but should not be at all close to the radiator. You can stack more or less of the cushions to get the proper height of the rad shell for alignment of the rad shell, hood and body.
Hope this helps.
