Tom, Your 300E requires a battery size known as group 27. In the early days, these batteries batteries put out about 450 Cold Crank Amps (CCA). Now, most modern group 27's have the ability to put out higher CCAs, in the range of 700 or so, as you mentioned in your email. Cold Crank Amp ratings provide the maximum battery amperage output possible at 0 degrees F. With The hard start conditions you describe, you are experiencing heat soak within the engine. Once it has been shut down for a while, the internal engine temp actually goes up for a bit before it starts to cool down. Assuming your battery and charging system is working properly, a larger battery and or higher output alternator will not solve your problem. My suggestion is to examine your battery cables first, and make sure they aren't a light gauge aftermarket type. Do they get hot when you crank the motor? The next consideration is the starter itself. The starter was offered with several different field windings, a small, a medium and a large type. all fit within the same starter type. When I was experiencing this problem with my 300G back in the '80s, I had the starter examined by a rebuilding shop that informed me that my starter had the light duty winding in it. The shop owner indicated that he could replace my light duty winding with a heavy duty winding (from a Dodge Power Wagon) and it would improve starter performance when the engine was hot. That is what I did back in '86 and I have not had a heat soak problem since. I believe this has been mentioned on the list in the past, and others have provided a part number for the heavy field winding. I would seek out a rebuilder in your area and ask him if he would rebuild your starter using the heavy winding. The rebuilder should be able to source the winding as well as install it. You'll be glad you did! Bob J 300G convert Danville, CA