The narrow part goes in first then you press it in until the shoulder is more or less level. I’ve not tried freezing, nor do I recall seeing that idea before. I don’t think it would help, if anything I suspect it might make it more difficult if it’s frozen rock solid. I doubt it makes it appreciably thinner and you do want some flexibility so it will compress slightly going through the neck. I’m not sure if warming to soften it would make much difference either. The clamp method always works well for me with a small block of wood nested semi-level on the other side. If you’re trying to avoid partially pulling the rad to get at the back side then maybe try fashioning a stick as a wood handle with the end sculpted to fit over the terminals. Wedging your body against the front of the car try pulling it toward you or maybe try using something like a length of 2x4 against the engine as a lever against the other end of the handle. I normally just do it dry unless I’m having a problem. If you’re half careful and the side tank should ever crack doing this I would expect that rad was due to soon fail anyway.
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Dave -still with 940's, prev 740/240/140/120 You'd think I'd have learned by now