Cereal Mash question

When doing a beer with a large amount - say 25% - of cereal adjunct such as maize or rice, I have been doing a preliminary cereal mash with some of the base malt, to convert the cereal first before adding it into the main mash. I have been doing this at 71 °C = 159.8 °F, the reason being that I want to be in alpha amylase territory to zap the cereal more effectively. This of course produces a sort of dextrin soup so the question is:

When I pour the resulting mush into the main malt mash, to get 64 °C = 147° F does the beta amylase in the main mash then start to attack the dextrins etc and turn most of them into fermentables?

You don't do a cereal mash to convert the starches you do it to gelantinize them. The real conversion is then done in the main mash. A small portion of malt in the cereal mash is just to provide a few enzymes to keep the mixture loosened up a bit. The temperature of the cereal mash should actually be brought up higher, even to boiling, to maximize the breakdown of the grains and the solubility of the starches. This higher temp range is then going to de-nature whatever enzymes are present in the mix limiting the amount of conversion. I'd think that many of the unintended long chains produced will be further broken down at the lower main mash temp.

Thanks Ed, so I'll just keep ramping up to boiling then let it cool down to the main mash temp and stir in.