How to trace an energy versus time diagram?
Assuming you want to plot heat exchanged by reaction versus time, you need at least to know what reaction you want to study. Then you will have to assess two different quantities: enthalpy if the process is isobaric (thermodynamic) and reaction rate (kinetic). This kind of data can be found on NIST Database.

If you do not find reaction enthalpy $\Delta_{R} H$, you can assess it by using enthalpies of formation:

$$ \Delta_{R} H = \sum\limits_i \nu_i h_{\mathrm{f},i} $$

Where $i$ indexes reactants and products, $\nu_i$ are stoichiometric coefficients (note: they are negative for reactant) and $h_{\mathrm{f},i}$ are enthalpies of formation. 

Then you need to find out which is the kinetic $v$ of your reaction and solve the related differential equation. If you do not find any information you might try the activated complex model:

$$ v = \frac{1}{V}\frac{\mathrm{d}\xi}{\mathrm{d}t} = k(T)\prod_j x_j^{\alpha_j} $$

Where $\xi$ is the molar coordinate of your reaction (De Donder variable), $k(T)$ the kinetic constant, $x_j$ are reactant concentrations and $\alpha_j$ are partial orders of reaction (they can be taken equals to $|\nu_j|$). Solving this differential equation - for a given set of initial conditions - will provide you a relation, maybe explicit, between $\xi$ and $t$.

Merging both step results will lead to enthalpy-time expression which can be plotted. Of course those calculation might be perform numerically.

If you were looking for an hand-made and pedagogic Energy Plot like this, you have not searched so far.

Method exposed above does not create this kind of plot which shows internal energy of sum of compounds versus coordinate of a molecular transformation. Gap between the initial and final state is the energy relaxed/absorbed by the reaction (often pure heat). Such plot are arbitrarily plotted because the activated state is often unknown and definitely non measurable. Furthermore everything between initial and final state is also not-well-known because we just have access on macroscopic data so we ignore microscopic details. Last hint: activation energy (maximum) is always higher than the higher state, you need extra energy to initiate the transformation.