Without the temperature regulation of those guts, now the temp will run differently with different loads and speeds, but stopped and at idle, with a good fan and pump, the water temp should actually fall.If it doesn't rev it up to 1000 rpm and watch the gauge. If the temp does not fall, either buy or build a hi-flo pump.(The anti-cav plate used to be sold separately). If buying, I have a 16 year old Milodon hi-flo pump,and matching stat, still in action; so of course I recommend them.
My 360 runs 14* idle timing. It has a 276/286/110 cam in it and a 750DP on an AG with unwrapped TTIs. It runs a rock-solid 205*.It idles at 750.I hear the thermostatic clutch kick in occasionally, after a hard run, but mostly it's pretty quiet.And since I like to rev the berries off it, I run an underdrive crank pulley and an overdrive alternator pulley. in an effort to keep the belt on. I have never yet thrown a belt.
I run a restrictor in my bypass hose too. My theory was, that after the stat opens this forces the water to go to the rad. If you notice, the later intakes have a bigger bypass system. I choked mine down to the old size . It seems to work.
Your rad size should be fine. I run a 26" A/C rad from a 73 Swinger 318, in a resized core-support. Yeah it's old, and it is only a 2-row.I guess she's pushing 44 this year. Yours looks all shiny and new. I imagine her calling out to that 340;"common big boy, show me what you got!"