The Urim and the Thummim were put into the breastpiece of the high priest. Urim means flame or light. Thummim means perfections. The purpose of the Urim and the Thummim was to enable the high priest to inquire for the LORD’s judgment about important situations. It is not known how the process worked, but it seems probable that questions were asked which could be answered by a yes or no answer. Possibly if the answer was “Yes”, the Urim would glow and if the answer was “No”, the Thummim would glow. This is partially speculation, although we know that the answer wasn’t given by the priest pulling out the Urim & Thummim for a yes or no answer as in drawing lots, because in 1 Samuel 28:6 we read that when Saul inquired of the LORD, the LORD did not answer by Urim.
And when Saul inquired of the LORD, the LORD did not answer him, either by dreams, or by Urim, or by prophets.
So to answer your question, there is no indication at all in Scripture that the priest could look into heaven by means of the Urim and Thummim. There is also no indication that the priest could literally hear from heaven when consulting God through the Urim and Thummim. It is more likely, as I mentioned before, that the Urim and Thummim glowed to provide an appropriate answer to the question.
These are the references to the Urim and Thummim in Scripture: Exo 28:30; Lev 8:8; Num 27:21; Deut 33:8; 1 Sam 14:41; 1 Sam 28:6; Ezra 2:63.