Will my UK T-mobile iPhone 5s work with a US T-mobile sim?

I'm going to the US in August for 2 weeks, and I'm hoping to get a US sim card so I can use data whilst I'm there. I'm currently on T-mobile in the UK on my iPhone 5s, and I'm wondering if I need to unlock my iPhone before heading to America, or if a US T-mobile sim will work on my phone anyway.

I'd preferably use T-mobile in the US because they have a "pay per day" deal, where you pay $2 a day for unlimited texts, calls and data. I'm doing this for the data though, as it's much cheaper than purchasing a bolt-on in the UK.

Nope. It would have to be unlocked for that to happen. Despite them being under the same name T-Mobile US & UK are 2 different carriers.