Whit smoke out the tail pipe?

Leaking cylinder head gaskets can show up with multiple symptoms, but white smoke from the tail pipe is the most common, due to burning antifreeze. Head gaskets seal passages for coolant, oil under pressure, oil draining back, and combustion. Coolant and oil are under very low pressure. Cylinder pressure is very high, so when the head gasket corrodes, it's most common for combustion gases to get pushed into the cooling system passages.

What is less common is for that smoke to clear up after the engine warms up. It can happen, but most of the time that smoke continues or gets worse as the engine gets warm.

A common test for this is to use a "leak sniffer" at the radiator cap. Here's links to some related articles:

https://www.2carpros.com/articles/head-gasket-blown-test

https://www.2carpros.com/articles/recognizing-the-symptoms-understanding-a-blown-head-gasket-in-your-vehicle

https://www.2carpros.com/articles/complete-guide-to-removing-and-installing-automotive-engine-cylinder-heads

The first one shows this test being done. You can usually borrow the tool from an auto parts store that rents or borrows tools, but be aware, they usually make you buy your own bottle of special fluid. That is because it is rendered ineffective if it freezes or if it gets coolant mixed in with it. They don't want to risk borrowing the tool to you after the previous person contaminated the fluid. You may need to suck some coolant out of the radiator to prevent some from getting sucked into the tester. As you draw air from the radiator through the tester, if combustion gases are in the coolant, the test liquid will turn from dark blue to bright yellow. If it does, you can return the fluid to dark blue for another test in the future by drawing fresh air through it for a minute or two.

You can even check if the fluid is active by "talking to it". Hold it up high enough, then exhale into the port as you suck air through the tester. The carbon dioxide in your breath will turn the fluid bright yellow.

Normally the fastest and least expensive repair is to replace the head gaskets. It's standard practice to replace both of them at the same time. Less common would be to find a crack in one of the cylinder heads. Given the symptom the smoke only occurs at startup, it could mean the leak is so small, you're only seeing the little that seeped out when the engine was stopped and there was still a little pressure in the cooling system. If you can't find the leak in the gaskets or heads, the best approach would be to have the heads inspected at an engine machine shop. Sometimes a small leak in a head will open up or close from engine heat, making the leak hard to spot without special equipment. One of the tricks they use is a special dye that shows up in cracks with a black light. The people at those shops can give you more advice. There are some cases where it is very common for cracks to develop, yet they routinely get dismissed because we know they won't cause a problem. It's just as bad to replace a head for one of those types of cracks while overlooking the true cause of the leak.

You'll want to check the heads for flatness too. That requires a precision straightedge and very thin feeler gauges. Multiple measurements must be taken in different areas and directions, and the specs are different between aluminum and cast iron heads.

Another common symptom, when the leak gets worse, is engine overheating. That can occur when combustion gases sneak into the cooling system and pool under the thermostat before it has opened. Thermostats have to be hit with hot liquid to open. Hot air won't do it. When the thermostat remains closed, hot coolant can't flow to the radiator.

In my opinion, the least desirable repair would be to replace the entire engine. You could get a perfectly fine-running replacement that develops the same problem soon. This is riskier when the used engine doesn't come with a history. You don't know if the coolant was replaced regularly. That is done because it's the additives that wear out in about two years. One of those additives is a corrosion inhibitor which is important in reducing the chance of a head gasket leaking due to corrosion.

Keep me updated on how this repair goes.