The anhydrous is fine to use, but you have to take account of its lower molecular weight. Don't get scared about the complicated sounding name though, its pretty simple.
Look on wikipedia, mag chloride 'molar mass' is:
95.211 g/mol (anhydrous)
203.31 g/mol (hexahydrate)
So for one mole (just think of a mole as 1 'unit') the hexahydrate needs 203 grams, the anhydrous needs only 95 grams for the same actual quantity of mag chloride (the difference in weight is, as you said, water). So if you want to know how much anhydrous to use, do:
95/203 = 0.47 times as much. So use 0.47 kg of anhydrous mag chloride to replace 1 kg of mag chloride hexahydrate.
BTW personally I would never use the volume to measure (ie a cup), so I suggest weighing the hexahydrate and anhydrous and doing it by weight, really don't recommend using the 0.47 factor for volume because the density might be different for the 2 forms of mag chloride. Once you have weighed it once and worked out the volume you need that way I guess its OK to measure by volume but still, IMO its not that reliable, I do everything by weight personally. Since you will need less anhydrous, any errors would be magnified too.
edit: forgot to say, don't think the heat will be a problem, if youre concerned add mag chloride to water, not water to mag chloride, and do it slow. Add a few grams and stir and see if it gets warm. Do a bit more etc. Go slow first time basically.