The Tynecastle side started the campaign minus 15 points and with a registration embargo after lapsing into administration with many tipping them for relegation.
However, after four Scottish Premiership games they have reduced their negative points tally by seven while also beating Raith Rovers on penalties in the second round of the Scottish Communities League Cup on Tuesday night.
The Gorgie boss, though, mindful of the fact that skipper Danny Wilson and left-back Kevin McHattie are suspended for the trip to Inverness on Saturday, brought a sense of perspective into his club's encouraging start.
"Our only target was to get to zero points as quickly as we could," said Locke.
"At the start of the season I think everybody, quite rightly, would probably have said Hearts are going to get relegated.
"We have had a reasonable start but that's all it is. It is only four games in.
"We said that to the players after the other night (League Cup).
"It was a great battling performance but we haven't achieved anything.
"The main thing was to get a win early for the supporters, who have been fantastic.
"We have managed to pick up a few points but just because we have had a reasonable start, we still have a huge mountain to climb.
"I think that is the most important thing, we don't get too carried away.
"But we have given ourselves a little chance and hopefully the boys can keep putting in the performances they are putting in at the moment.
Locke is hoping keeper Jamie MacDonald will shrug off an ankle injury picked up against Raith.
He said: "Jamie is not looking too bad. He went over on his ankle and got a wee shock but it has settled down well and I am hoping to have him available at the weekend.
"We are down to the bare bones. It is the same squad of players minus two so it will be really difficult.
"I can't afford to lose anyone from the squad, it is small enough as it is."
- Sports & Recreation
- Raith Rovers
- Scottish Premiership
- Danny Wilson