Simulink - two variables assigned to a flow path

I would like to model and study a simple hydronic system with a handful of pipes randomly branching and merging. I would randomly assign and vary the flow rates and temperatures of the fluid and I would like to observe how those properties change throughout the network.

The two parameters are governed by two simplest expressions, based on whether a node is merging or diverting: q_1 + q_2 = q_3, and q_1 * t_1 + q_2 * t_2 = q_3 * t_3, where q is the flow, and t is the temperature.

I imagine Simscape can do this but it looks like an overkill, and I would like to try and model this by hand in Simulink instead so I can learn the basics better. What would be the best approach to simulate this in Simlink? I am not asking for ready models, just a guidance for which direction to pursue. Everything I tried so far makes me think I need to model parallel flow paths, one for the flow rate q and the other for the temperature t, but I'm wondering if there is a simpler way to combine them inside a common function, or something like that.

[Walter Roberson]

Well, if you are not using Simscape Fluids, if you are doing it directly in Simulink, then the easiest approach might be to model the network as an electrical network. For example, model increasing cross-sectional area of each pipe as the reciprocal of resistance.

[Milos Krsmanovic]

I don't even need to size the pipes, do anything with velocities or pressure drops, etc. The only thing I'm after is how the temperature of a pipe/section changes in different parts of the network as flows merge and divert, and that is driven by the flow rate and temperature that I would explicitly assign.