You may specify the ice temperature as well. Let's say it is at 0 degree. There will be a heat transfer from the hot water toward the cold ice. The water temperature will certainly decrease and a quantity of your ice will start to melt. we need more numerical data if you want to know the water temperature.

( 1 st,there is no such physical represenatation of heat, heat is a manifestation of a temperature gradient)

I believe the process will follow the phase diagram for water.

the water will lose energy to the energy sink ( the dry ice) remIning in the liquiidmphase.

it will remain at 0 c, until the last molecule of the liquid water leaves 0c for the colder temperature.

at this point the water will become a solid, and now become colder than 0c, losing energy to the sink

I accept with Dr Abdallah. Moore data are needed to analyze your case.

Regards

@Abdallah I mean dry ice i.e., solid co2

Is there any chance that sublimating co2 will disrupt the formation of ice particles and the water temperature may drop below 0c

We can do a thought experiment. Consider an adiabatic reactor at 1 atm ( volume can vary). Let the volume of water initially at 0C be V_w, and the volume of dry ice be V_i=V_w cc. Take the density of dry ice to be rho_i=1.5 g/cc and the density of water rho_w=1gm/cc. Now the heat of sublimation of dry ice at 1 atm and 25C is 571J/gm. Let us us this value in our thought experiment.

Now in our adiabatic reactor all the heat of sublimation must come from the water at 0C. The heat of fusion of water is 334 J/g Thus in our adiabatic reactor we require DeltaH= 334*rho_w*V_w=(334*V_w) J to freeze all the water. The enthalpy released when the dry ice sublimes is DeltaH=1.5 *571*V_i > 334*V_w.

Thus the ice will be sub cooled if the pressure of the reactor is maintained at 1 atm.

This is a crude calculation of the process.

Brian is (very nearly) correct under his assumptions. The problem statement never said that the system is adiabatic and that is a major problem with the original question. If the system is open, the final answer is 25°C, but there is no way of determining what will be the temperature transient without more information.

It is an open system. If the water temperature stays at 25c how come instant icecream can be made by adding dry ice to the icecream batter.

I didn't say that there wouldn't be a temperature transient, just that, if the experiment was performed at room temperature, eventually the whole system would be a room temperature.  Yes, you can make ice cream, but leave it alone and it will melt.  My whole point was that the question was not well defined.  There are lots of questions asked here that are similarly ill defined.  If the problem is left open you can make any assumption that you want to complete the problem definition and get any answer that you want.

I feel there may be a slight decrease in temp of water as dry ice will sublime not melt. you will get CO2 bubbles coming out of water thats it.

So, being that I just received some lovely omaha steaks in the mail, I had some dry ice to casually experiment with. Not exactly scientific, but I poured about a liter of water into a pot and added ice cubes until the water reached approximately freezing. I think dropped in a few large chunks of dry ice. After bubbling for a few minutes, the bubbles almost stopped, to the point where I decided to take the ice out of the pot and see what had happened. It turns out that once it reaches 0c, the dry ice will form a layer of regular ice around it, preventing it from sublimating further, except for a small holy that each piece of dry ice had formed, which continued to slowly bubble. The water did not freeze over (as I had hoped), and instead continued to have this small layer of ice around the dry ice until the dry ice was gone entirely. Speeding up the process was the fact that when the ice reached a certain thickness, the whole piece floated to the surface and began to melt faster. Not exactly a scientific experiment, with plenty of room to experiment, but interesting never the less.

Mr. Robichaud's experiment is interesting, in fact I have done the same thing, but like me, he probably used a great deal  more water than ice.  For the requested case of equal volumes of water and dry ice, things are different.  1 cc of dry ice has an enthalpy of sublimation of 767J.  The heat of fusion of 1 cc of water is 335J so if combined adiabatically the water will freeze and cool below it's freezing point. Since the heat capacity of ice is about 0.5 cal/gm*C it would take 164J to cool the ice to the sublimation temperature of CO2 so the adiabatic system would end up at the sublimation temperature of CO2