If you do something without a second thought, you do it without first considering if you should do it or not.

She'll spend a hundred dollars on a dress without a second thought. 她会毫不犹豫地花100美元买一条裙子。

to change your opinion about something or start to doubt it

You're not having second thoughts about getting married, are you? 结婚的事你没改变主意吧？

used when you want to change a decision you have made

Can I have a cup of coffee, please? - actually, on second thoughts, I'll have a beer. 请来杯咖啡——说实话，我改主意了，来杯啤酒好了。