Here's an article from WHFoods.com citing several sources from well-respected journals that says that "Research studies have shown that the healthy omega-3 oils and lignan phytonutrients in flaxseeds are surprisingly heat stable. Not only is it safe to leave whole flaxseeds at room temperature but you can also use them in baking." This is mainly true of the ground flax, but not the oil.
Here's a couple articles they cite:
Hyvarinen HK, Pihlava JM, et al. Effect of processing and storage on
the stability of flaxseed lignan added to bakery products. J Agric
Food Chem. 2006 Jan 11;54(1):48-53.
Manthey FA, Lee RE, Hall CA 3rd. Processing and cooking effects on
lipid content and stability of alpha-linolenic acid in spaghetti
containing ground flaxseed. J Agric Food Chem. 2002 Mar
As you probably know, flax seed has tons of benefits besides fiber including omega-3's, anti-cancer and anti-inflammatory properties. It's what they feed chickens to make those omega-3 eggs.
In general, using whole flax seeds is pretty pointless from a nutritional standpoint, as we don't really digest them (maybe if you really chew them really well :).
A great list of the benefits of flaxseeds can also be found on this site.
For another good vegetarian source of fiber and omega-3's, check out chia seeds which you can mix into water for a healthy drink, add to food, or use like flax seed as thickener.