This is a good question. The answer is, "It depends".
I think you need to separate the data into two categories. You only need the values for volume and moles to calculate the K for the reaction. They each have 3 sig. figs so you are justified to use three significant figures for K. Now temperature is not directly included in the calculation of K so we need to consider T separately.
You could state that you know the value of K to 3 sig. figs but the relevant temperature is only +/- 0.5 degree C because that is the instrumental uncertainty if you quote T = 60. Does that help?