1997 Chevy S-10 10 degree increase under acceleration

Change the coolant temperature sensor (cts).

Check the resistance of the CTS, and compair it to the corresponding sensor spec. The CTS and the IAT change resistance as the coolant (cts) or air (iat) heats up and cools.
Also, make sure the A/C condenser is clear of debris. The condenser is in front of the radiator, and debris can block air flow to the radiator.

Did this happen before or after the radiator change? Be sure that there is coolant in the reservoir.

Ok, I assume that you have confirmed that coolant is flowing through the engine when the t-stat opens up -- right. So, being that you have changed everything - confirmed that coolant is flowing when t-stat opens -- brings me to this point. Coolant gets hot when the t-stat holds it in the engine until a certain temperature is acheived (usually around 180 degrees or so). Then the t-stat allows the coolant to flow - thus the upper radiator will get hot and it will pressurize. - I am sure you know this -. Now, if the coolant flow is blocked or restricted from flowing through the radiator, then the coolant will absorb too much heat from the engine. I think you may have a restriction in the coolant flow, internally, in the engine. Being that everything is new - (the radiator, water pump, all the hoses) - the only thing left is to flush the engine block out by removing the water pump again, and flushing the block with some presurized water through the water ports on the block. The water should flow out just about at the same pressure as it goes in -- if not -- remove the soft plugs in the block and flush again to find the blockage (if there is one).
Also, try changing the radiator cap -- it may be stuck.

What type of scan tool are you checking the timing with?

Ah yes -- "orange sludge" rears it's ugly head once again. That is the effect of GMs' version of Dexcool (the orange coolant). Your radiator is new so you shouldn't want any of the sludge that is in the engine to break free and clog the new radiator and /or the water pump - (and it will). To be honest, it is only a matter of time before you need to replace the lower intake manifold gaskets, so I would just go ahead and remove the water pump - flush the crap out of the system with a high pressure hose. Then remove the soft plugs and flush again the same way. Most of the sludge should come out of the soft plug holes - and this will totally flush the entire engine block -- but not the heads. The heads is where this sludge really causes problems - and probably yours. The build up is usually most around the number 7 and 8 cylinders (the back of the engine). The best way to clean up the heads is to remove them -- but you can also just remove the lower intake manifold (which will need to be done soon anyway) and very carefully clean and flush out the heads that way. Then replace the lower intake gaskets (and be sure to use the new, more expensive, style gaskets with the metal inserts to prevent over torqueing).
A radiator flush may or may not do the trick.I know it seems extreme and it is a lot of work, but if the blockage gets worse, it can distort the cylinder bores (from uneven heat dissipation) and cause the head gasket or even the piston rings to fail prematurely. Be sure to put new soft plugs in the block useing gray silicone - and allow at least a day before you put coolant in the engine (this will allow the soft plugs to properly seal). Use Prestone Dexcool coolant - not GM Dexcool. Mix it properly or just buy it premixed.

The scan tool is a good tool for the home mechanic, but it cannot tell you where the timing of the engine is at. It just tells you the spark advance or retard degree from the base timing point. The base timing point (which is +or- 1 degree of TDC) is set by adjusting the distributer and using a GM Tech One scan tool. Timing lights will not work. These scan tools are not usually not available outside of a dealership and they are around $15000.00 bucks. Anyway, I don't think it is a timing issue -- it probably is a blockage in the cooling system caused by GM Dexcool (the orange coolant). BTW - google 'gm dexcool settlement'. You may be suprised.

Flush the block through the water pump ports and soft plugs - as I described - and then remove the lower intake manifold (and the heads if you so desire).

It's not a lower end tear down -- it's just the intake. If you have already replaced the injector unit then it should be pretty easy. Leave the upper intake manifold (the plastic cover over the injector unit) bolted onto the lower intake -- just remove the lower intake bolts - 4 on each side - to remove the lower "intake". Your intake system has an upper and a lower. The upper part can remain on when the lower is removed. Just don't over torque the lower bolts when you put it back on.

Your engine is showing all the signs of (what I call) GM Dexcool destruction. The temp. Rise, plugged radiator, and now failing lower intake gasket are all of the typical signs. There is no doubt about it now - you must replace the lower intake gasket ASAP. The coolant will eventually leak into the oil and before you know it, your engine will have non-repairable damage. I am sure you know oil and engine coolant DO NOT mix.I do suggest the following (only because it is only a little more work and you will have the intake removed) remove the heads and replace the head gaskets and valve seals. It is only a little more work and it is relatively easy to do. You can get a total kit which includes lower intake gaskets, head gaskets, head bolts, valve seals, and everything to complete the job. Fel-pro makes the kit.
Some tips are: always clean the head bolt threads (in the block) with a tap, get some copper seal spray from permatex and spray it on both sides of the head gaskets (let it dry before installing), DO NOT over tighten the lower intake bolts (spec is 88 INCH pounds which is like 7 foot pounds), use gray silicone for the front and rear sealing of the lower intake -- and allow at least 24 hours for the silicone to dry.

One more thing -- use prestone dexcool coolant in the engine. It is not the GM version and works much better than GMs' version.