Choice of model/strategy for multiple regression analisys


I am doing an econometrics course where I am to do a regression analysis on some firm data.
I want to analyze some shipping data of frozen goods to predict the temperature of the shipped goods at their end destination.
My problem is that I am unsure which kind of analysis to make when I am interested in both time-variant and in-variant variables

My data:
I have approx 100 data points for different shipments. For each data point, I have the starting temperature of the products (same for all) and the end temperature after arriving at their end destination. That is my dependent variable. Additionally, I have data for 4 other independent variables:
kg of dry ice (In-variant)
kg of products shipped (In-variant)
time of shipment in days (time-variant)
Ambient temperature during shipment (In-variant)

My model is then:
The temperature of the shipped products = kg of Dry Ice + kg of Products + Time + Ambient temperature

Because of my Time variable, I believe that I should du a Panel Data analysis. But as I also want to estimate the effect of some in-variant variables I should use a Random effect approach.

Am I correct in my reasoning?

Or could i simply just frame the model as Cross-sectional not taking into account the time periods (as all shipments have the same starting temperature)
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I suggest you take a look at the following material to better understand the difference between fixed and random effects. In brief, you should (a) have some theoretical reasoning describing relationships between your time-variant and invariant predictors, then (b) run both FE and RE models and examine consistency of the estimates, and finally (c) conduct a formal Hausman test to assess which model is more appropriate (looking to observe consistency with your theoretical reasoning).