Refer to heat transfer texts to find the best relationship you can for heat transfer by natural convection for the situation- treat it as a plate or sphere or whatever is close. Then assume your widget is all at the same temperature. You can then equate the time rate of change of temperature to the difference in temperature between the widget and the surroundings. This lets you solve for temperature as a function of time.
We did this way back in an ME lab to ascertain how long a thermocouple needed to remain in the surroundings before it read the "right" temperature. This is not expected to be an accurate method, but a ballpark method, with the uncertainties in the convective heat transfer being the biggest problem.
If you go through this process and it shows you reach equibrium in 10 minutes or in 20 minutes, it may not be too meaningful, as the inaccuracies could be too great. But if it shows that the equilibrum is reached in 30 seconds or takes 4 hours, that would be more meaningful.