340 Cold Valve Lash Unknown Cam

If the correct lash is unknown, then you certainly do NOT want to set lash at 028/032". Many modern grinds use 018 -020" lash. Ultradyne [ now Bullet ] use 016 lash. Setting lash way too large slams the lifter into the cam flanks, & not the clearance ramps as designed, shock wave to the valve train.
For safety & long parts life with an unknown cam, you should set the lash to 012 - 014. It will not hurt anything but may idle rougher & lose some low end tq if cam was designed for 028/032 lash.
With experimenting I did on one of my 440s, stock head & block, I found no measurable difference in lash between room temp & operating temp.