That indicates a problem with the overdrive system (not the cooling system). Keep in mind the OD system should engage at 55 deg C (131 deg F) so even a stuck open engine thermostat will allow the van to warm up enough to activate the system. If your heater works correctly (blows hot air) then your coolant temp is definitely above 55 deg C.
When the van fails to go into overdrive, the 1st thing to do is check the 7.5A fuse in the top center of your fuse box:
This fuse also supplies power to your gauges and some of your warning lights, so if that stuff works then it's probably not it, but it's easy to check so you should check it anyhow.
If the fuse checks good take off your center console and inspect all of the wires in this area. Make sure they are all connected securely and free of damage. Note: shorted or grounded wire(s) in this area can prevent your OD from working, so make sure the wires have separation (not pinched together) and make sure the wire insulation is intact with no exposed copper. Pay particular attention to the blue/white wires and the little blue box that sits up in front of the shifter (under the console cover). That box is your overdrive relay (on 2wd vans only). Note: the 4wd van has a slightly different / more complicated OD system, but since yours is a 2wd we'll stick to 2wd for the sake of this discussion.
Here's the relay used on 2wd vans:
Here's the harness that goes to the switch:
Make sure it's hooked up to this plug coming from the shift mechanism. Note: two of the wires inside this black protective tube are the OD switch wires. Since the switch side wires (actual wires coming from the shift lever switch) are subject to change color, always identify them by tracking them up to the shift lever or identify by the wire color on the "van side" of the harness. The colors on the harness are wht/blk & orange. One thing worth noting. The switch does not turn-on the OD (it actually limits it). Electrically speaking, when the switch is closed, the OD will not work and the "O/D OFF" indicator light will illuminate. When the switch is open, the "O/D OFF" light will go out and the van will be free to shift into OD (assuming there are no other issues).
If the relay and wires in this area are hooked up and look good, then remove the passenger seat, peal back the carpet and remove the big engine access panel (Instructions on how to remove are covered
HERE). Once off you will have access to your OD thermo switch.
Here is it's location:
The thermo switch is N/C (Normally Closed). When the van is cold (less than 55 deg C) it grounds out the OD circuit preventing the transmission from shifting into OD. Once the coolant temp hits 55C the switch opens and that enables the OD circuit. Because of the way Toyota set it up it's easy to bypass the thermo switch. All you need to do is unplug the gray harness connector to the thermo switch and that's it! If the thermo switch is the problem, then the OD system will now be active.
If disconnecting the thermo switch doesn't work, then you'll need to check the OD solenoid on the transmission. It's on the drivers side of the tranny here:
It is grounded through the transmission and is activated by a single wire. Here is where that wire connects to the harness:
And here is the connector position when installed in the van:
Before you get involved with testing components make sure the solenoid is in good physical condition and verify it's hooked up to the van wire harness. Trace the wires as far as you can to verify there's no physical damage to them either.
If you are unable to resolve the problem at this point, let me know and I'll walk you through component level troubleshooting. Tim