The thermal cutout pops on tank two after it shuts off. It boils then shuts off. It also turns off when taking a shower, producing cold water. I checked the ohm readings on the thermal cutout and the heating elements. everything seems to read correctly.

It *may* not be a problem with the water heater itself necessarily. When you say "keep adjusting the water temperature when you're taking a shower" I presume you're talking about turning the shower hot/cold knob(s) and not the temp thermostat on the water heater itself.
If so, when it starts to run colder, turn the knob all the way to full hot. Is the water then very hot? If so, the water heater is working fine & doing its job, and the problem is likely to be in the shower faucet mixing valve itself. Sometimes a faulty one will expand the inner seals/cartridge as hot water flows thru it, and starts to (wrongly) restrict the hot water flow, thus causing the constant need to "turn the dial up a notch".

For clarity, a Furnace produces HOT AIR for heat while a boiler produces HOT WATER for heat. Just remember...boil = water. You said your "furnace" does not produce hot water for a shower and because furnaces do not product hot water unless they have some model that do???? Usually people with a furnace have a seperate hot water heater. People with boilers though can produce hot water for use as both their sinks/showers hot water and their heat (by heating water that goes through baseboards) in their house. I don't believe any furnaces produce hot water most of the time a furnace just produces hot air for heating. So figure out what you first have.
Having said that, I'll assume you have a boiler like I do and my Weil McClean(sp?) stopped working a while back and wasn't turning on to "boil" any water. I took apart the burner and there is a light sensing photo resistor as part of the controls. If this phto resistor goes bad, the boiler will not start. The resister is cheap, I think it was $8 but you have to know what you're doing to change it. So you may be better to call someone who can work on such equipment.
Boiler's themselves are not overly complex. Home heating oil is the same diesel fuel that you can buy in a gas station only the government has "oil" companies put a RED die in home heating fuel which is usually cheaper then Diesel fuel because diesel fuel is taxed to death. The reason they do that is so that if you try putting RED tinted home heating fuel in your truck and you get pulled over (because you're a trucker with and 18 wheeler and they typically do inspections of these trucks) you will be a huge fine if they see you're running home heating fuel and NOT paying your taxed by purchasing Diesel fuel. A little bit of background so you know the fuel you are dealing with here. So it's dieslel fuel without the tax you run in your boiler. Gasoline on the other hand is VERY explosive as you know, but diesel fuel (if you're ever tried to light it) takes some coaxing to get lit. When it's cold out, diesel fuel is very hard to light and that's why trucks use glow plugs. You don't need those in your home though.
But because diesel fuel/home heating oil is hard to light, it's sprayed as a msit into your boiler, so that it can light more easily.
But because it is a fuel, you should know what you're doing when messing with it. FInd out what you have, and then have someone work on the issue if you haven't already. I'm guessing you have had it fixed by now?

The left canister probably has a grounded element in it, which will keep power going after the water is off. Either that or you have a bad triac on your control unit

Popping sound is caused by sediment built up in bottom of tank: air bubbles get trapped when heating starts, and then they crackle, rumble etc when free.
Clean out sediment:
http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html
http://waterheatertimer.org/pdf/How-to-descale-water-heater.pdf
The steps vary by type of water heater, gas or electric

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

You've done the required first-step troubleshooting and maintenance.
If thermal cutout keeps tripping, and unit is actually reaching 185, then something is wrong with wiring, temperature sensor, gas valve, or PC board. Or combination of factors.
Call service technician, and open following link for some Bosch tankless resources including Bosch contact information:
http://waterheatertimer.org/Troubleshoot-Bosch-Tankless-water-heater.html

This should run two showers at once with no problem. If you have a shut off valve on the cold side of the heater, try closing about halfway. This will slow the water flow and the water will have more time to heat up as it pases through the tank. If you dont have a shut off valve, just cut back the hot water valve on your shower and do not use any cold water. If it gets too hot then turn on a little cold water. The object is to slow the speed of the water going through the tank. Tankless heater take a little getting use to but they work great when you know how to treat them. On my shower I turn the hot all the way on until it gets hot and then add a little cold water to bring the temp down. You may have too much water going through too fast to be able to heat it up to what you need. Try this and see how it works.

Not sure but check the inlet water at the heater, the filter may be clog up a little that restrict the flow. Did u use the heater at all during the winter? If not, the heat exchanger may be clogged with built up in there. U need to descale it. Good luck. Chinhcu

WE THOUGHT WE NEEDED ANOTHER THERMOSTAR, BUT WHEN WE WERE LOOKING FOR THE PART THE EMPLOYEE ASKED WHAT WAS THE TROUBLE. WE EXPLAINED, HE SAID YOU DEFINATLY DO NOT HAVE A PROBLEM WITH YOUR TANK AND ASKED IF WE HAD A SINGLE HANDLED FAUCET WITHIN THE HOUSE. NO WE DONT. HE SAID IT SOUNDS LIKE WATER IS MIXING WITH THE COLD WATER THATS THE REASON FOR THE WARM--COLD--WARM WATER. COME TO FIND OUT SINCE WE ARE REMODLING THE BATHROOM, WE HAD BOTH THE HOT AND COLD WATER TURNED ON IN THE SHOWER--BUT WERE PLUGGED OFF AT THE SHOWER HEAD AND THE FAUCET UNTIL THE TILE IS INSTALLED. SOOO ALL MY HUSBAND HAD TO DO WAS TURN OFF THE WATER IN THE SHOWER. NOW WE HAVE PLENTY OF HOT WATER, NO WARM COLD. YEA!!!

there is a little cap on the hot and cold side above the shut off valves, turn the water off at these valve and take the caps off there are filters in there clean them off and reinstall them that should take care of the problem, you might want to flush the tank while your at it hook a hose to the hot side connector and run it out side or to a sump pump then turn on the cold water and flush it out you can also reverse this procedure by doing it on the cold side