Is our sense of smell heightened when we are asleep? My question is whether our sense of smell is stronger when we sleep? From an evolutionary perspective this could have been beneficial in terms of runaway camp fires, marauding saber tooth tigers or the testosterone of night-raiding cave men. 

Does this effect back off when we wake, as our eyesight comes into play? And, if so, how do we account for the claims that many people die in  night time house fires before they wake up?

I'm aware that the brain is able to desensitise itself to certain smells and go about its olfactory business elsewhere. That second sniff of fresh-ground coffee beans is never as good as the first.  I'd say that most people assume they are 'a bit slow' first thing in the morning until they 'wake up properly', but is this true?
Short answer
The sense of smell may still be operational during sleep, but it is not enhanced. Olfactory stimuli typically will not wake you up during sleep, however.

Background
Olfaction and sleep are an interesting lot. Most sensory stimuli presented during sleep typically cause awakening, especially when when they are intense  and sudden (e.g. a loud noise). This is not the case with odors, and even holds for unpleasant ones (Carskadon &amp; Herz, 2004). 

In addition, while most sensory systems stop processing their input altogether, odors remain processed by the sleeping brain. This may, at least in part, be due to the direct olfactory projections from the periphery to the cortex, without a thalamic relay being used as with the other senses (Perl et al., 2017). However, they will typically not wake a person up.

The neural adaptation (reduction of sensitivity over time) of the olfactory system is related to repeated or sustained exposure to scents (Dalton, 2000), and it is not affected by sleep per se as far as I know. Hence, taken together these findings support the claim that odor alarms will not work.

Note, however, that fire comes with heat and irritant smoke that will work on the heat and pain receptors in the skin, respectively. These may wake you up, barred the dulled sensory systems pick the stimuli up. And even then it may already be too late to be of any help.

References
- Dalton, Chem Senses (2000); 25(4): 487-92
- Carskadon &amp; Herz, Sleep (2004); 27(3): 402-5
- Perl et al, Springer Handbook of Odor: 111-2