Answer
The temperature rise per minute would be $4.8\times10^3 C^{\circ}$ without cooling water.
Work Step by Step
Assume that all of the electrical energy fed into the x-ray tube transforms into heat energy.
$$P=IV=\frac{Q}{t}=\frac{mc\Delta T}{t}$$
We measure power in joules per second, so the kcal units in the specific heat should be converted to joules. Find the temperature rise per minute.
$$\frac{\Delta T}{t}=\frac{IV}{mc}=\frac{(0.025A)(95000V)(60s/min)}{(0.065kg)(0.11kcal/(kg\cdot C^{\circ})(4186J/kcal))}$$
$$=4.8\times10^3 C^{\circ}/minute$$
Obviously, the cooling water is essential.