Overheating issue?

My check engine light is on, and my thermostat light will come on while on hills and highway, but flashes then shuts off once my foot is off the gas. I have a little rough start up on cold mornings (being my mornings are 35°F) it sounded like the spark plugs were going, so I replaced those and the coil packs. I still get a rough start but it's fine after a few seconds. Now my temp light comes on every now and then. Which obviously freaks me out until I notice it shut off when I release the gas pedal. Took it to a mechanic who used to work at Toyota and said I need a new heater exchange which I can't find online. Is he wrong or am I not looking for the correct part?