Stainless steel handles a very wide temperature range — that’s part of why it’s trusted in professional kitchens. Here’s what’s safe, plainly.
Hot food, going in: no problem. You can put hot food straight into a food-grade steel container; it won’t warp, melt, or leach the way plastic can. Let the lid cool slightly before sealing a hot container so a vacuum doesn’t make it hard to open.
Oven: some steel containers are oven-safe (often up to around 200°C+), but the lid and any silicone seal are not — remove them first, and only use the oven if the maker says the body is rated for it.
Freezer: steel is freezer-safe. Leave a little headroom for food that expands, and you’re set.
Microwave: this is the one no. Metal blocks microwaves — plate your food to reheat.
The temperature-sensitive part is the seal. Food-grade silicone tolerates a broad range but is the component to protect from direct high heat (like an oven). The steel body is the tough part.
Carrying hot or cold: for keeping food hot or cold for hours, a double-walled insulated container or bottle does that job; a standard single-wall container holds temperature briefly but isn’t insulated.
Short version: steel is safe from freezer to oven for the body, with two rules — no microwave, and take the seal out before any oven use.
Food should be stored without doubt.