Temperature Uncertainty

The water experiment did not repeat very well due to the amount of water in the beaker and the hot plate starting temperature.
Therefore, every trial has very different values at the same times.
Should we treat the data as if each trial was supposed to be the same (i.e. take averages of values taken at the same time) and get huge errors?
Or should we use the thermometer temperature as a metric instead of the time (i.e. take averages of thermocouple values taken at the same thermometer reading)?

If there are significant differences between the two runs based on how you conducted the experiment, then you might consider splitting the runs out, i.e. showing thermocouple vs. thermometer run 1 and thermocouple vs. thermometer run 2. That would probably make the error bars more reasonable for each individual water bath run, and also gives you an opportunity to comment on the repeatability of the measurements for each device (size of the error bars in each run). The only disadvantage to doing it this way is that you might have 4 curves on one plot, which could get a bit crowded once error bars are added in. Just make sure in this case that the plot looks 'nice' and I can easily tell which curve corresponds to which test (as I'm the one ultimately grading the report). Your group might even consider doing subplots, with one thermocouple vs. thermometer run per subplot. Definitely a lot of possibilities...you'll have to decide which one you think looks best and most effectively presents the data.