The basal metabolic rate (BMR) is the "minimum energy expenditure for the body to exist" (Guyton & Hall, 2000). In other words, even when we're completely at rest, the body still needs to spend some of our hard-earned energy reserves on keeping us ticking. This is fairly obvious once you think about it: just because you want to loaf on the couch for a bit, this doesn't mean, for example, that your heart and lungs can take a complete break too! The BMR does not include the energy that you expend on physical activity, or even on metabolising food.
And the relation of the BMR to our body temperature? Well, all the body's metabolic processes unavoidably produce some heat as a byproduct. (For those interested, this is predicted by the second law of thermodynamics.) Thus, the higher the BMR, the more heat that is generated, and the higher the body's potential internal temperature.
'Potential'. To function properly, the body requires a fairly constant internal temperature. Thus, if the BMR isn't producing enough heat to keep the temperature 37.0ºC, other methods must be used. These include shivering - which is a series of involuntary muscle contractions. The body doesn't care one bit whether you look silly as you shake, what it's after is the heat generated from the chemical reactions required to contract a muscle.
Another strategy used to raise the temperature is sending a message to the person's consciousness, making him/her feel cold. This is in the hope that the person will use behaviour to help raise the temperature. For instance, the person may put on a jersey, or move indoors where it is warmer. That's why a low BMR can make you feel cold. Your body is having to bring your behaviour in to help it stay warm, and the only way it's got to tell you is via the physical sensation of coldness.
Incidentally, some of you may know that people with an under-active thyroid gland (hypothyroidism) often complain of coldness. This is directly related to all of the above, since the thyroid hormones normally increase the basal metabolic rate. So someone complaining of chronic coldness is often tested for thyroid disease.
The BMR varies quite a lot between people normally, however. For example, it depends partly on age, sex, climate, and body mass, amongst others. For a rough estimate of your BMR (emphasis on rough), go here: http://health.discovery.com/tools/calculators/basal/basal.html