Dimensional analysis of the heat transport through ducts filled with saturated He II is extended to pressurized conditions up to 20 bar. Simplified models are also presented for the ease of first order estimation of the GM-transport heat flux density, the temperature gradient and the limiting heat flux densities by relating calculations to reduced thermo physical properties, with respect to the properties at the lambda point. The data available show good support for the dimensionless GM-equation in pressurized He II within data scatter and thermo physical property uncertainty. (C) 2004 Elsevier Ltd. All rights reserved.