Normally, volumetric water content of soil increase with the depth. For a peatland, it depends on the heterogeneity of the media but for each profile of water content, you should have a correlation with the profile of heat flux. Anyway your question is not totally clear for me! What do you mean of "average". Will you develop your question more?

Thanks for your interest in the question! Generally, what I want to know, is what shape the volumetric water content profile attains in the precipitation-free periods in a peatland. By "average peatland" I mean any peatland having peat depth>1m and no special features in the peat structure, hydrology, etc.

The problem is essentially that I do not know, whether the theta-profile decays exponentially, linearly or logarithmically between the peat surface and the water table.

Good, I understood well your problematic now. So I suggest you to have look at:

1-Benscoter et al. (2001) Interactive effects of vegetation, soil moisture and bulk

density on depth of burning of thick organic soils.

Which is freely accessbile and I think it's very useful for you, because they talk about VWC profile and heat profile at the same time in some organic soils.

and

2-Leon Etienne Parent, Piotr Ilnicki, "Organic Soils and Peat Materials for Sustainable Agriculture" page 56.

Thanks for the help! So, it seems that the theta profile is approximately negative-logarithmic, just as I suspected.