In general it is impossible for ordinary people to enter heaven like that. But the special cases mentioned by @iammilind are different. There is no Vedic ritual which will enable any Jiva atma to ascend to heaven in sthula sharira under ordinary, mundane causes. But there is a story of Trisanku who does ascend, which is another special case.
Valmiki Ramayana Bala Kanda
tasya buddhiH samutpannaa yajeyam iti raaghava || 1-57-11
gacCheyam sva shariireNa devaanaam paramaam gatim |
vasiSTham sa samaahuuya kathayaamaasa cintitam || 1-57-12Oh, Raghava, an idea sprang up in the mind of Trishanku to perform a ritual by which he will go to heaven with his own body. Then he sincerely invited Vashishta and told him what his thinking is.
ashakyam iti ca api ukto vasiSThena mahaatmanaa |
pratyaakhyaato vasiSThena sa yayau dakSiNaam disham || 1-57-13
tataH tat karma siddhi artham putraan tasya gato nRipaH |But the great-souled Vashishta said it as impossible. Thus repudiated Trishanku went to southerly direction in search of orchestrators for the purpose of realizing that task, such a phantasmal ritual that enables him to go to heaven with his body, and that king has gone to the sons of Vashishta.
....
....
....
sa shariirasya bhadram vaH trihankoH asya bhuupateH |
aarohaNam pratij~naatam na anRitam kartum utsahe || 1-60-27"'Let safety betide you all. I have promised to this king Trishanku that he will ascend to heaven with his mortal body, and I am not interested to make it untrue.' (Spoken by Vishwamitra to the Gods)
svargo astu sa shariirasya trisha.nkoH asya shaashvataH |
nakSatraaNi ca sarvaaNi maamakaani dhruvaaNi atha || 1-60-28
yaavat lokaa dhariSyanti tiSThanti etaani sarvashaH |
yat kRitaani suraaH sarve tat anuj~naatum arhatha || 1-60-29"'Let there be eternal heaven to Trishanku with his mortal body. Next, as along as the worlds remain, let all of these stars and galaxies I have created also remain eternally in their places as my creation. It will be apt of you all gods to accede to this.' So said VishvamitraVishwamitra to gods.
evam uktaaH suraaH sarve prati uucuH muni pu.ngavam |
evam bhavatu bhadram te tiSThantu etaani sarvashaH || 1-60-30
gagane taani anekaani vaishvaanara pathaat bahiH |
nakSatraaNi muni shreSTha teSu jyotiHSu jaajvalan || 1-60-31
avaag shiraaH trishankuH ca tiSThatu amara sannibhaH |"When all the gods are addressed thus they replied the eminent saint VishvamitraVishwamitra saying, 'so be it! Safe you be! Let all the created objects prevail in their respective places. Those amazing and numerous stars you have created will remain in firmament, but outside the path of stelliform of Cosmic Person. Trishanku will also remain in the circle of stars you created, but upside-down, for Indra's indict cannot be annulled, and he will be gleaming like a star and similar to any celestial.
There is also a case when King Raivata entered Brahmaloka just like that, with Revati, his daughter, to find a suitable groom for her. This story however, is most commonly used as an example for time dilation, when thousands of years on earth had passed just when it seemed like 20 minutes in Brahmaloka.