In previous games, to get rematches with trainers, you used the VS Seeker to see if the trainers were willing to battle. In HeartGold & SoulSilver however, the rematches are done a different way. Firstly, only a few dozen trainers in Kanto & Johto are capable of being battled again.

In order to get the rematch, you have to receive the PokéGear number from the trainer in question. Then, on a certain day, you will need to ring the trainer in question to organise a rematch. It is not guaranteed that a rematch will be discussed when you call but keep trying and you should get it. Below is a list of all the trainers, battleable on Thursday, and their teams including their first team and each team's increase in level. Click the other days to go to their page

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday

Thursday

Time Location Trainer
Morning
4am-10am
Johto - Route 44 Fisherman Wilton
Teams

First Battle
Fisherman Wilton Goldeen Goldeen Seaking
Level 26 Level 26 Level 28
Sceond Battle
Fisherman Wilton Goldeen Goldeen Seaking
Level 32 Level 32 Level 36
Third Battle
Fisherman Wilton Goldeen Seaking Seaking
Level 32 Level 36 Level 40
Fourth Battle
Fisherman Wilton Seaking Seaking Seaking
Level 42 Level 46 Level 63
Morning
4am-10am
Kanto - Route 26 Ace Trainer Gaven
Teams

First Battle
Ace Trainer Gaven Victreebel Kingler Flareon
Level 32 Level 32 Level 32
Second Battle
Ace Trainer Gaven Victreebel Kingler Flareon
Level 34 Level 34 Level 34
Third Battle
Ace Trainer Gaven Victreebel Kingler Flareon
Level 38 Level 39 Level 38
Fourth Battle
Ace Trainer Gaven Victreebel Kingler Flareon
Level 52 Level 49 Level 50
Day
10am-8pm
Johto - Route 32 Picnicker Liz
Teams

First Battle
Picnicker Liz Nidoran ♀
Level 8
Second Battle
Picnicker Liz Weepinbell Nidorina
Level 35 Level 38
Third Battle
Picnicker Liz Weepinbell Nidorino Nidoqueen
Level 39 Level 38 Level 40
Fourth Battle
Picnicker Liz Weepinbell Nidoqueen Nidoqueen
Level 47 Level 58 Level 60
Day
10am-8pm
Kanto - Route 12 Fisherman Kyler
Teams

First Battle
Fisherman Kyler Magikarp Magikarp Magikarp
Level 18 Level 18 Level 18
Second Battle
Fisherman Kyler Magikarp Magikarp Magikarp Magikarp
Level 18 Level 18 Level 18 Level 18
Third Battle
Fisherman Kyler Magikarp Magikarp Magikarp Magikarp Magikarp
Level 18 Level 18 Level 18 Level 18 Level 18
Fourth Battle
Fisherman Kyler Magikarp Magikarp Magikarp Magikarp Magikarp Magikarp
Level 18 Level 18 Level 18 Level 18 Level 18 Level 18
Night
8pm-5am
Johto - Route 38 Lass Dana
Teams

First Battle
Lass Dana Flaaffy Psyduck
Level 19 Level 19
Second Battle
Lass Dana Flaaffy Golduck
Level 32 Level 31
Third Battle
Lass Dana Golduck Ampharos
Level 36 Level 38
Fourth Battle
Lass Dana Golduck Ampharos
Level 51 Level 54
Night
8pm-5am
Kanto - Route 15 Teacher Hillary
Teams

First Battle
Teacher Hillary Sunkern Aipom
Level 41 Level 31
Second Battle
Teacher Hillary Ambipom Sunflora
Level 43 Level 43
Third Battle
Teacher Hillary Ambipom Sunflora
Level 49 Level 49
Fourth Battle
Teacher Hillary Ambipom Sunflora
Level 55 Level 55
 
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