This article will first discuss the problem of the temperature transient analysis, the flow conditions and the assumptions required to sufficiently simplify the thermal model so that existing solutions can be applied, and their applicability confirmed. Secondly, we will discuss some closely related problems whose solutions are already available, along with the modifications required to apply them to our case. The article continues with a numerical study that was carried out to check the applicability of the existing (modified) solutions. We will either include, or discuss, all the relevant physical phenomena affecting the flowing fluid (Joule-Thomson effect, transient thermal expansion, friction losses, and multi-dimensional heat losses). Finally, a novel approach for the calculation of semi-steady state heat losses from a reservoir to the surrounding formation will be presented. It is based on the solution to the 鈥渉ot fluid injection鈥?problem with appropriate corrections.