The MP for Penrith has been the surprise star of the party contest so far on social media, with videos of him meeting the general public while touring towns across the country being shared widely on Twitter.
Stewart, a former diplomat who has travelled across Asia and the Middle East, has also attracted headlines for his colourful personal life before he entered the Commons in 2010.
Last week he apologised for smoking opium while travelling in Iran 15 years ago, admitting that it was a “very stupid mistake”.
The MP has sought to present himself as a unity candidate to the Conservative membership, and last week claimed he wanted to set up a Citizens’ Assembly to thrash out a Brexit compromise.
But as his campaign gathers momentum online, opposition party activists have been scrutinising his voting record during his nine years in parliament.
Stewart has been criticised by anti-Brexit campaigners for consistently voting against a right to remain for EU nationals already in living in the UK.
The independent website TheyWorkForYou, which tracks all of the UK’s MPs, shows that he has voted 15 times against such bills since 2016.
The site notes that on the vast majority of issues, Stewart votes the same way as other Conservative MPs.
The leadership hopeful has advocated a tough approach to welfare. He has generally voted for reducing housing benefit for social tenants deemed to have excess bedrooms - the so-called Bedroom Tax - while almost always voting against paying higher benefits over longer periods for those unable to work due to illness or disability.
On social issues, Stewart has voted for equal gay rights. He has three times voted against smoking bans.
When it comes to the constitution, Stewart is a well-known supporter of the Union and campaigned for a No vote at the 2014 referendum.
Following the publication of a Scottish Government bill which could pave the way for an IndyRef2, Stewart said: “In everything we do and everything we say in this leadership race we should remember that the key is to unify the country and not divide the United Kingdom”.
On other matters, he has almost always voted for reducing central government funding of local government and consistently voted for fewer MPs in the House of Commons.
The Tory leadership contest will offically begin when Mrs May resigns as party leader on June 7.