Your description of the basal metabolic rate is spot on, and it is indeed equated with the amount of heat you give off.
The way to look at this is yesterday I weighed 60kg and today I weigh 60kg, but in between I've consumed about 2,500 calories. That energy must have gone somewhere. Since I'm the same today as I was yesterday there's no net energy change in me, so either I must have put the energy into making chemicals that I've excreted, or I must have radiated it as heat.
Actually the energy won't all have gone as heat. For example I synthesis sebum and excrete it through sebacous glands where it rubs off on my clothes or gets washed off in the shower. If you burnt the sebum the heat you'd get back would have to be included in the 2,500 calories, but as dmckee says, it's hard to believe this is a significant part of the energy balance. I suppose you should also include the bile and enzymes my gut secretes, and which leaves me every morning, but in the interests of good taste let's not go there :-)
You're quite right that energy is used in cell maintenance, but then I get back energy by metabolising the old cells. The point is that I'm basically the same as I was yesterday so there has been no net energy change.
Of course there are circumstances where the food intake doesn't all go as heat. My teenage niece eats more than she radiates and puts the energy into growing at an improbable rate. My brother also eats more than he radiates and puts the energy into growing his beer belly at an improbable rate!