I bought a car, now it turns out the transmission needs work, and we would like to get a professional's opinion. The engine light came on and I was trying to accelerate to 40 mph, but the RPMs were at 5000. We think it's the transmission solenoids. Now our car is overheating when we have the AC on at the stop light. Any suggestions? PS when I bought the car, it didn't hesitate to pick up speed at all.
There's a few things going on here, and they may or may not be related.
Check Engine Light This means the computer has found something wrong with something and has stored a "trouble code" in it's memory. Most auto parts stores will read these codes for free, that should get you started.
Overheating Make sure you have enough coolant. Your coolant should have a MIN line on the side, make sure your coolant is above that. If it's low, add the appropriate coolant (get it from an auto parts store). Then turn the car on with the hood raised, wait for the engine to reach it's normal temperature and then stand there looking at the radiator fan until it starts. You may need to wait several minutes. If the engine temperature climbs above it's normal range (overheating) and the fan doesn't come on, this is your overheating problem.
Transmission Solenoids are simple and inexpensive to replace on many vehicles. It would help your diagnosis if you could narrow it down to which specific solenoid may have gone bad. You need to know how many gears the automatic transmission has. Most Kia Rios have 4, some have 6.
Go for a drive and keep track of which gear the car is likely in (this is a lot easier on empty roads, so I suggest you do this very early in the morning or very late at night). Make sure you are in "D", and first use very mild (10% pedal) acceleration, see if the transmission shifts up every single gear without running the RPMs past 3000 rpm. If the RPMs do go above 3000 rpm, take note of which gear the transmission is in at that point.
Next, use harder acceleration (50% pedal). The RPMs should run higher before shifting, this will make the gears easier to track. Again, note which gear the transmission is in if the RPMs are getting higher than in another gear. The reason for this test is that different solenoids control different shifts, if only 1 or 2 of them are not working well, this is likely the cause.